This document contains an MBA thesis presented by Hikmet Tagiyev Sakhavet at Khazar University in Baku, Azerbaijan in 2007. The thesis examines actuarial analysis in social security systems. It discusses topics such as demographic projections, financial projections using the present value technique, and life tables. The research objectives are to identify economic criteria for analyzing social security systems and pension reform in the context of population aging, and to quantify the effects of demography, pension systems, and pension reforms on future poverty and inequality for aging countries.
The document outlines two sessions on risk management in banking and finance. Session 9 will cover risk measures, regulatory aspects, and basic principles, including defining risk measures, academic vs accounting standards, desirable properties, and estimating risks from samples. Session 10 will cover correlations, copulas, modeling dependencies between risks, diversification effects, comparing risks under dependence vs independence, and analyzing individual risk contributions. Examples of applications to finance, environmental risks, and credit risk are also provided.
Robust Calibration For SVI Model Arbitrage FreeTahar FERHATI
This document outlines a study on interpolation and extrapolation methods for implied volatility slices and surfaces under arbitrage-free conditions. It introduces the Stochastic Volatility Inspired (SVI) model, which provides a parametric fit for implied volatility data. The SVI model is chosen for this study due to its closed-form formula and ability to fit equity market data. The document also discusses the convergence of the Heston stochastic volatility model to the SVI model at large times.
This document describes a study that jointly estimates a proportional hazards model and stochastic frontier model to assess the effect of inefficiency on bank failure probability. It begins with an introduction noting the limitations of existing two-stage approaches. The methodology section outlines the models, priors, and Bayesian estimation procedure. Simulation results show the joint approach performs better than two-stage maximum likelihood. The application analyzes U.S. bank data from 2001-2010, finding statistical evidence that inefficiency significantly impacts failure time.
On Foundations of Parameter Estimation for Generalized Partial Linear Models ...SSA KPI
1) The document discusses estimation methods for generalized linear models (GLMs) and generalized partial linear models (GPLMs). 2) GPLMs extend GLMs by adding a single nonparametric component to the linear predictor. 3) Parameter estimation for GPLMs is performed by maximizing a penalized likelihood function, where the penalty term controls the tradeoff between model fit and smoothness of the nonparametric component. 4) An iterative algorithm such as Newton-Raphson is used to solve the penalized maximum likelihood estimation problem.
The document discusses the design of a fuzzy logic traffic controller for ATM networks. It describes how fuzzy logic is implemented using rules and defuzzification methods to generate outputs. The rules are optimized using genetic algorithms and simulation shows improvement over traditional methods. Fuzzy logic controllers are based on fuzzy sets and linguistic variables. Rules relate input and output variables using terms like "low" and "medium". The MAX-MIN inference method is used to determine output membership functions from the rules.
Lesson 14: Derivatives of Logarithmic and Exponential FunctionsMatthew Leingang
The document is a lecture on derivatives of exponential and logarithmic functions. It begins with announcements about homework and an upcoming midterm. It then provides objectives and an outline for sections on exponential and logarithmic functions. The body of the document defines exponential functions, establishes conventions for exponents of all types, discusses properties of exponential functions, and graphs various exponential functions. It focuses on setting up the necessary foundations before discussing derivatives of these functions.
The document is a lecture note from an NYU Calculus I class covering the definite integral. It provides announcements about upcoming quizzes and exams. The content discusses computing definite integrals using Riemann sums and the limit of Riemann sums, as well as properties of the definite integral. Examples are given of calculating Riemann sums using different representative points in each interval.
The document discusses measures of dispersion such as variance, standard deviation, and the coefficient of variation. It defines variance as the average squared deviation from the mean and standard deviation as the positive square root of the variance. The coefficient of variation measures relative dispersion by dividing the standard deviation by the mean. It is unit-free and allows for comparison across distributions. The document also covers Chebyshev's inequality and how it relates to the proportion of data within a given number of standard deviations from the mean.
The document outlines two sessions on risk management in banking and finance. Session 9 will cover risk measures, regulatory aspects, and basic principles, including defining risk measures, academic vs accounting standards, desirable properties, and estimating risks from samples. Session 10 will cover correlations, copulas, modeling dependencies between risks, diversification effects, comparing risks under dependence vs independence, and analyzing individual risk contributions. Examples of applications to finance, environmental risks, and credit risk are also provided.
Robust Calibration For SVI Model Arbitrage FreeTahar FERHATI
This document outlines a study on interpolation and extrapolation methods for implied volatility slices and surfaces under arbitrage-free conditions. It introduces the Stochastic Volatility Inspired (SVI) model, which provides a parametric fit for implied volatility data. The SVI model is chosen for this study due to its closed-form formula and ability to fit equity market data. The document also discusses the convergence of the Heston stochastic volatility model to the SVI model at large times.
This document describes a study that jointly estimates a proportional hazards model and stochastic frontier model to assess the effect of inefficiency on bank failure probability. It begins with an introduction noting the limitations of existing two-stage approaches. The methodology section outlines the models, priors, and Bayesian estimation procedure. Simulation results show the joint approach performs better than two-stage maximum likelihood. The application analyzes U.S. bank data from 2001-2010, finding statistical evidence that inefficiency significantly impacts failure time.
On Foundations of Parameter Estimation for Generalized Partial Linear Models ...SSA KPI
1) The document discusses estimation methods for generalized linear models (GLMs) and generalized partial linear models (GPLMs). 2) GPLMs extend GLMs by adding a single nonparametric component to the linear predictor. 3) Parameter estimation for GPLMs is performed by maximizing a penalized likelihood function, where the penalty term controls the tradeoff between model fit and smoothness of the nonparametric component. 4) An iterative algorithm such as Newton-Raphson is used to solve the penalized maximum likelihood estimation problem.
The document discusses the design of a fuzzy logic traffic controller for ATM networks. It describes how fuzzy logic is implemented using rules and defuzzification methods to generate outputs. The rules are optimized using genetic algorithms and simulation shows improvement over traditional methods. Fuzzy logic controllers are based on fuzzy sets and linguistic variables. Rules relate input and output variables using terms like "low" and "medium". The MAX-MIN inference method is used to determine output membership functions from the rules.
Lesson 14: Derivatives of Logarithmic and Exponential FunctionsMatthew Leingang
The document is a lecture on derivatives of exponential and logarithmic functions. It begins with announcements about homework and an upcoming midterm. It then provides objectives and an outline for sections on exponential and logarithmic functions. The body of the document defines exponential functions, establishes conventions for exponents of all types, discusses properties of exponential functions, and graphs various exponential functions. It focuses on setting up the necessary foundations before discussing derivatives of these functions.
The document is a lecture note from an NYU Calculus I class covering the definite integral. It provides announcements about upcoming quizzes and exams. The content discusses computing definite integrals using Riemann sums and the limit of Riemann sums, as well as properties of the definite integral. Examples are given of calculating Riemann sums using different representative points in each interval.
The document discusses measures of dispersion such as variance, standard deviation, and the coefficient of variation. It defines variance as the average squared deviation from the mean and standard deviation as the positive square root of the variance. The coefficient of variation measures relative dispersion by dividing the standard deviation by the mean. It is unit-free and allows for comparison across distributions. The document also covers Chebyshev's inequality and how it relates to the proportion of data within a given number of standard deviations from the mean.
MBA thesis presentation: design strategies and brandingVizuarna
This document discusses a thesis on corporate design strategy and branding, and the role of design management in developing corporate identity. It includes a three-part agenda: 1) the motivation for the thesis, 2) key findings regarding branding, corporate identity, and corporate design strategy, and 3) future directions such as design management becoming a corporate culture and strategic partner to business. There is also an overview of the corporate identity audit process involving preparation, execution, and results.
This document outlines a thesis investigating Greek business strategy during an economic crisis through qualitative and quantitative analysis. The thesis will examine the correlation between strategic firm characteristics and financial performance using questionnaires and financial statements from Greek companies. Statistical analysis will be conducted on the questionnaire responses and companies will be segmented into high-tech and non-high-tech. A qualitative comparative analysis method called fuzzy set qualitative comparative analysis will also be used to identify combinations of factors that led to profitable and sustainable businesses during the crisis period. The research aims to identify a "crisis resilience" business profile.
The document proposes developing an interactive interface to teach adults basic technology skills, such as using computers and software. The goal is to remove fears around technology and make it desirable for adults to learn. Visual prototypes would be created to simply explain how to use computers. Learning technology empowers adults and allows them to better communicate with loved ones, as technology is now essential for many tasks. The project has potential to travel beyond the classroom and help many people learn technology basics.
Digital marketing for cloud services_Master's thesis resultsStephanie Schulze
B2B digital marketing‘s influence on organisational buying behaviour and its key success drivers for promotion of cloud computing services - An empirical study as part of a Master's thesis
Ph.D Thesis Defense: Magnetic Reconnection as a Chondrule Heating MechanismSamuel Lazerson
Samuel Lazerson defended his PhD thesis examining whether magnetic reconnection in a dusty plasma could explain the heating of chondrules. He conducted the first simulations of magnetic reconnection in a dusty plasma using the DENISIS code. The simulations initialized a Harris current sheet that underwent ballistic relaxation into an equilibrium state. Magnetic reconnection then occurred, and test particle simulations examined chondrule heating. The thesis aimed to provide a self-consistent model for chondrule formation via magnetic reconnection in a dusty plasma environment like the early solar nebula.
This document outlines key concepts about consumer behavior from marketing textbooks. It discusses factors that influence consumer behavior such as cultural, social, personal, and psychological factors. A model of consumer behavior is presented involving need recognition, information search, evaluation of alternatives, purchase decision, and post-purchase behavior. Maslow's hierarchy of needs and theories of motivation from Freud and Herzberg are also summarized. The document provides an overview of the consumer decision process.
Impact of green marketing on customer satsifaction and environmental safety -...Kartik Mehta
In recent years, concern about the environment has been highlighted in many areas of life. Our limited resources are damaged, the future of human life disturbs this planet, thus leaders and thinkers have to create a solution. The influence of green marketing tools have been analysed in this study, namely the eco-label, eco-brand and environmental advertisement. The sampling used was available cluster sampling. Tehran city is divided into four parts, North, South, East and West. The western and northern areas of the city were selected and we distributed our questionnaire. The sample size was 384 people.
Formulae and data was analysed using the Spearman correlation test and multiple regression analysis. The results show that environmental advertisement had the most significant effect on consumer purchasing behavior and eco-brand had the least effect.
Pvh2010 09-28 apollon - sme living lab experiencePiet Verhoeve
This document discusses an SME company called Televic's participation in the Apollon European living lab project. Televic produces healthcare communication products. They test products technically on live networks, evaluate user responses, and validate introduction models in living labs. For the Apollon project, Televic aims to evaluate their products in new environments in Finland, validate technical circumstances, and explore new markets with the help of a local Belgian academic partner and European living labs. So far they have found the process of transferring products to a new country challenging but valuable for validating business models in different healthcare systems.
El poema describe cómo el silencio de una persona revela aspectos de su carácter, como la lealtad, la fortaleza, la impotencia, el miedo, la sabiduría, la cobardía y la prudencia. Finalmente, señala que el silencio permite la meditación de los sabios pero también es el refugio de los cobardes.
Este documento é uma transcrição da música "The Prayer" de Celine Dion e Andrea Bocelli com tradução para o espanhol. Contém as letras da música pedindo a Deus que nos guie e proteja, nos dê fé e esperança, e nos leve para um lugar seguro.
Dwyer Insurance provides homeowners insurance policies customized to each client's needs and circumstances. The document outlines several factors that determine policy ratings and pricing, such as home characteristics, coverages selected, and client history. Optional add-on coverages are also described. Dwyer Insurance emphasizes the importance of consultation to evaluate all relevant details and ensure policies are tailored to fully protect each client.
International Business (IB) consists of all commercial transactions between two or more countries and involves the exchange of goods, capital, services, and other economic resources across national borders. Studying IB is important because most companies either operate internationally or compete with international companies. The modes of operations and best practices for conducting business may differ between countries. Understanding IB helps with career decisions and determining what governmental policies to support.
El documento discute el perfil del ingeniero de sistemas del futuro y actual. Se argumenta que debe ser global, con habilidades de comunicación multilingüe y trabajo en equipo. También debe tener una visión holística e involucrarse en la adopción de nuevas tecnologías. Para el ambiente actual de negocios, se requiere conocimiento de organizaciones y habilidades gerenciales de proyectos. En los próximos 5 años, se define al ingeniero como un profesional con formación integral, ética, autonomía, pensamiento crítico y conocimientos
The document proposes creating a 21st Century Technology Theatre at the ABC International School. The theatre would consolidate cutting-edge technologies currently dispersed around the school into one centralized location. It would house equipment like MacBooks, iPads, microphones, a SmartBoard, and sound system. This would create an inspiring environment for creative student presentations and lessons where teachers could incorporate different technologies. A budget is included outlining the costs of additional equipment needed to complete the theatre. Floor plans show the layout and include a wiring closet to provide network access to all devices in the space.
This document discusses trends in membership for associations and concerns about maintaining membership levels over the next 5 years. It notes that 44% of associations saw higher membership over the past 5 years but only 15% expect higher membership going forward. The biggest concerns about future membership include an aging membership and attracting youth. Charts show that the typical association membership age is shifting upwards. The document argues that associations need to focus on the customer value proposition by providing exclusive benefits that address specific needs and by reworking structures and strategies to enhance the membership value.
This document is a product guide from M-Audio that provides information on their various audio equipment offerings in 2009. It includes sections on DJ tools, audio interfaces, studio monitors, microphones and preamps, software, and contact information. The product guide contains details on specific M-Audio products within each category such as the Torq DJ controller, ProFire audio interfaces, Studiophile studio monitors, and Pro Tools recording software. Contact information is provided for M-Audio locations in the US, UK, Canada, and Japan.
Predictive Modeling in Insurance in the context of (possibly) big dataArthur Charpentier
This document discusses predictive modeling in insurance in the context of big data. It begins with an introduction to the speaker and outlines some key concepts in actuarial science from both American and European perspectives. It then provides examples of common actuarial problems involving ratemaking, pricing, and claims reserving. The document reviews the history of actuarial models and discusses issues around statistical learning, machine learning, and their relationship to statistics. It also covers model evaluation and various loss functions used in modeling.
This document discusses demographic forecasting using functional data analysis. It presents a functional linear model to model and forecast age-specific demographic rates like mortality and fertility over time. The model represents rates as curves that vary annually based on common age patterns, principal components of variation, and residuals. The document outlines how the model can be used to analyze outliers, produce functional forecasts, forecast groups of populations, and generate population forecasts.
MBA thesis presentation: design strategies and brandingVizuarna
This document discusses a thesis on corporate design strategy and branding, and the role of design management in developing corporate identity. It includes a three-part agenda: 1) the motivation for the thesis, 2) key findings regarding branding, corporate identity, and corporate design strategy, and 3) future directions such as design management becoming a corporate culture and strategic partner to business. There is also an overview of the corporate identity audit process involving preparation, execution, and results.
This document outlines a thesis investigating Greek business strategy during an economic crisis through qualitative and quantitative analysis. The thesis will examine the correlation between strategic firm characteristics and financial performance using questionnaires and financial statements from Greek companies. Statistical analysis will be conducted on the questionnaire responses and companies will be segmented into high-tech and non-high-tech. A qualitative comparative analysis method called fuzzy set qualitative comparative analysis will also be used to identify combinations of factors that led to profitable and sustainable businesses during the crisis period. The research aims to identify a "crisis resilience" business profile.
The document proposes developing an interactive interface to teach adults basic technology skills, such as using computers and software. The goal is to remove fears around technology and make it desirable for adults to learn. Visual prototypes would be created to simply explain how to use computers. Learning technology empowers adults and allows them to better communicate with loved ones, as technology is now essential for many tasks. The project has potential to travel beyond the classroom and help many people learn technology basics.
Digital marketing for cloud services_Master's thesis resultsStephanie Schulze
B2B digital marketing‘s influence on organisational buying behaviour and its key success drivers for promotion of cloud computing services - An empirical study as part of a Master's thesis
Ph.D Thesis Defense: Magnetic Reconnection as a Chondrule Heating MechanismSamuel Lazerson
Samuel Lazerson defended his PhD thesis examining whether magnetic reconnection in a dusty plasma could explain the heating of chondrules. He conducted the first simulations of magnetic reconnection in a dusty plasma using the DENISIS code. The simulations initialized a Harris current sheet that underwent ballistic relaxation into an equilibrium state. Magnetic reconnection then occurred, and test particle simulations examined chondrule heating. The thesis aimed to provide a self-consistent model for chondrule formation via magnetic reconnection in a dusty plasma environment like the early solar nebula.
This document outlines key concepts about consumer behavior from marketing textbooks. It discusses factors that influence consumer behavior such as cultural, social, personal, and psychological factors. A model of consumer behavior is presented involving need recognition, information search, evaluation of alternatives, purchase decision, and post-purchase behavior. Maslow's hierarchy of needs and theories of motivation from Freud and Herzberg are also summarized. The document provides an overview of the consumer decision process.
Impact of green marketing on customer satsifaction and environmental safety -...Kartik Mehta
In recent years, concern about the environment has been highlighted in many areas of life. Our limited resources are damaged, the future of human life disturbs this planet, thus leaders and thinkers have to create a solution. The influence of green marketing tools have been analysed in this study, namely the eco-label, eco-brand and environmental advertisement. The sampling used was available cluster sampling. Tehran city is divided into four parts, North, South, East and West. The western and northern areas of the city were selected and we distributed our questionnaire. The sample size was 384 people.
Formulae and data was analysed using the Spearman correlation test and multiple regression analysis. The results show that environmental advertisement had the most significant effect on consumer purchasing behavior and eco-brand had the least effect.
Pvh2010 09-28 apollon - sme living lab experiencePiet Verhoeve
This document discusses an SME company called Televic's participation in the Apollon European living lab project. Televic produces healthcare communication products. They test products technically on live networks, evaluate user responses, and validate introduction models in living labs. For the Apollon project, Televic aims to evaluate their products in new environments in Finland, validate technical circumstances, and explore new markets with the help of a local Belgian academic partner and European living labs. So far they have found the process of transferring products to a new country challenging but valuable for validating business models in different healthcare systems.
El poema describe cómo el silencio de una persona revela aspectos de su carácter, como la lealtad, la fortaleza, la impotencia, el miedo, la sabiduría, la cobardía y la prudencia. Finalmente, señala que el silencio permite la meditación de los sabios pero también es el refugio de los cobardes.
Este documento é uma transcrição da música "The Prayer" de Celine Dion e Andrea Bocelli com tradução para o espanhol. Contém as letras da música pedindo a Deus que nos guie e proteja, nos dê fé e esperança, e nos leve para um lugar seguro.
Dwyer Insurance provides homeowners insurance policies customized to each client's needs and circumstances. The document outlines several factors that determine policy ratings and pricing, such as home characteristics, coverages selected, and client history. Optional add-on coverages are also described. Dwyer Insurance emphasizes the importance of consultation to evaluate all relevant details and ensure policies are tailored to fully protect each client.
International Business (IB) consists of all commercial transactions between two or more countries and involves the exchange of goods, capital, services, and other economic resources across national borders. Studying IB is important because most companies either operate internationally or compete with international companies. The modes of operations and best practices for conducting business may differ between countries. Understanding IB helps with career decisions and determining what governmental policies to support.
El documento discute el perfil del ingeniero de sistemas del futuro y actual. Se argumenta que debe ser global, con habilidades de comunicación multilingüe y trabajo en equipo. También debe tener una visión holística e involucrarse en la adopción de nuevas tecnologías. Para el ambiente actual de negocios, se requiere conocimiento de organizaciones y habilidades gerenciales de proyectos. En los próximos 5 años, se define al ingeniero como un profesional con formación integral, ética, autonomía, pensamiento crítico y conocimientos
The document proposes creating a 21st Century Technology Theatre at the ABC International School. The theatre would consolidate cutting-edge technologies currently dispersed around the school into one centralized location. It would house equipment like MacBooks, iPads, microphones, a SmartBoard, and sound system. This would create an inspiring environment for creative student presentations and lessons where teachers could incorporate different technologies. A budget is included outlining the costs of additional equipment needed to complete the theatre. Floor plans show the layout and include a wiring closet to provide network access to all devices in the space.
This document discusses trends in membership for associations and concerns about maintaining membership levels over the next 5 years. It notes that 44% of associations saw higher membership over the past 5 years but only 15% expect higher membership going forward. The biggest concerns about future membership include an aging membership and attracting youth. Charts show that the typical association membership age is shifting upwards. The document argues that associations need to focus on the customer value proposition by providing exclusive benefits that address specific needs and by reworking structures and strategies to enhance the membership value.
This document is a product guide from M-Audio that provides information on their various audio equipment offerings in 2009. It includes sections on DJ tools, audio interfaces, studio monitors, microphones and preamps, software, and contact information. The product guide contains details on specific M-Audio products within each category such as the Torq DJ controller, ProFire audio interfaces, Studiophile studio monitors, and Pro Tools recording software. Contact information is provided for M-Audio locations in the US, UK, Canada, and Japan.
Predictive Modeling in Insurance in the context of (possibly) big dataArthur Charpentier
This document discusses predictive modeling in insurance in the context of big data. It begins with an introduction to the speaker and outlines some key concepts in actuarial science from both American and European perspectives. It then provides examples of common actuarial problems involving ratemaking, pricing, and claims reserving. The document reviews the history of actuarial models and discusses issues around statistical learning, machine learning, and their relationship to statistics. It also covers model evaluation and various loss functions used in modeling.
This document discusses demographic forecasting using functional data analysis. It presents a functional linear model to model and forecast age-specific demographic rates like mortality and fertility over time. The model represents rates as curves that vary annually based on common age patterns, principal components of variation, and residuals. The document outlines how the model can be used to analyze outliers, produce functional forecasts, forecast groups of populations, and generate population forecasts.
Calibrating the Lee-Carter and the Poisson Lee-Carter models via Neural Netw...Salvatore Scognamiglio
This document summarizes a research paper that develops a neural network model for large-scale mortality modelling of multiple populations. The model combines individual stochastic mortality models into a neural network environment that allows for information sharing between populations. This improves on traditional models that fit populations separately. The neural network model estimates parameters for modified Lee-Carter models in a single stage using all available data, producing more robust estimates and improved forecasting performance compared to traditional approaches. The model consists of three neural network subnets that estimate the age-specific, time-specific, and age-time interaction parameters of the Lee-Carter models for multiple populations simultaneously.
The document discusses key concepts in probability theory and statistical decision making under uncertainty. It covers topics like data generation processes being modelled as random variables, Bayes' rule for calculating conditional probabilities, discriminant functions for classification, and utility theory for making rational decisions. Bayesian networks and influence diagrams are introduced as graphical models for representing conditional independence between variables and making decisions. Finally, the document notes that future chapters will focus on estimating probabilities from data using parametric, semiparametric, and nonparametric approaches.
Value Based Decision Control: Preferences Portfolio Allocation, Winer and Col...IOSRjournaljce
The paper presents an innovative approach to mathematical modeling of complex systems „humandynamical process”. The approach is based on the theory of measurement and utility theory and permits inclusion of human preferences in the objective function. The objective utility function is constructed by recurrent stochastic procedure which represents machine learning based on the human preferences. The approach is demonstrated by two case studies, portfolio allocation with Wiener process and portfolio allocation in the case of financial process with colored noise. The presented formulations could serve as foundation of development of decision support tools for design of management/control. This value-oriented modeling leads to the development of preferences-based decision support in machine learning environment and control/management value based design.
Surveillance refers to the task of observing a scene, often for lengthy periods in search of particular objects or particular behaviour. This task has many applications, foremost among them is security (monitoring for undesirable behaviour such as theft or vandalism), but increasing numbers of others in areas such as agriculture also exist. Historically, closed circuit TV (CCTV) surveillance has been mundane and labour Intensive, involving personnel scanning multiple screens, but the advent of reasonably priced fast hardware means that automatic surveillance is becoming a realistic task to attempt in real time. Several attempts at this are underway.
New Mathematical Tools for the Financial SectorSSA KPI
AACIMP 2010 Summer School lecture by Gerhard Wilhelm Weber. "Applied Mathematics" stream. "Modern Operational Research and Its Mathematical Methods with a Focus on Financial Mathematics" course. Part 5.
More info at http://summerschool.ssa.org.ua
The document discusses using the programming language R for actuarial science applications. It presents R as a vector-based language suitable for working with life tables and performing actuarial calculations. Examples are given of how to model life contingencies like life expectancies, annuities, and insurance values using vectors and matrices in R. The document also discusses using R to fit prospective mortality models like the Lee-Carter model to data matrices.
These slides introduce the lifecontingencies R package functionalities. Pricing, reserving and simulating life contingent insurance will be shown. Similarly, joining Lee Carter mortality projections with demography R package and annuities evaluation with lifecontingencies R package is shown. The work has been all done with R markdown.
This document describes a doctoral thesis on using description logics and attribute vectors to represent ontological knowledge and perform reasoning. Description logics allow describing important domain concepts using concepts, roles, and logical relationships. The proposed approach uses subsumption relationships to build a dependency graph and generate vector representations of concepts. Reasoning algorithms using vector operations are presented to handle concept intersections, unions, and existential restrictions. It is argued that this approach simplifies reasoning and the algorithms are proven to converge over time. The thesis concludes the attribute vector representation carries semantic meaning and enables efficient reasoning implementation.
This document provides an overview of various classification techniques in data science, including linear discriminant analysis, logistic regression, probit regression, k-nearest neighbors, classification trees (CART), random forests, and techniques for double classification like uplift modeling. It discusses consistency of models and the risk of overfitting when the training sample size is small. Key classification algorithms like logistic regression and CART are explained in detail over multiple pages.
extreme times in finance heston model.pptArounaGanou2
Stochastic Volatility Models. 3. I - CTRW formalism. First developed by Montroll and Weiss (1965); Aimed to study the microstructure of random processe
Markov chain and SIR epidemic model (Greenwood model)writwik mandal
This document discusses Markov chains and the SIR epidemic model. It begins by defining random processes and Markov processes, noting that a Markov process is one where the future is independent of the past given the present state. It then introduces the basics of Markov chains, including the transition probability matrix. The document also explains the SIR epidemic model, which categorizes a population into susceptible, infected, and recovered groups. It provides the differential equations that model changes between these groups over time. Finally, it demonstrates how to model an SIR epidemic using a Markov chain with examples.
Qualitative Causality discovers potential causal relationships among the underlying phenomena for understanding, prevention, and planning using qualitative human understandable events rather than quantitative variables.
Bringing Deep Causality to Multimedia Data StreamsLaleh Jalali
This document outlines a framework for qualitative causality that combines data-driven and hypothesis-driven analysis. It describes using events extracted from multiple data streams to form qualitative causal patterns and models. An example application to asthma management is discussed where temperature, pollution, wind and other factors are analyzed for patterns related to asthma outbreaks. The framework allows gaining insights from both known and unknown questions by analyzing event patterns and hypotheses.
1) The document discusses how statistical learning techniques from other disciplines can inform econometric modeling and central bank policymaking.
2) It covers topics like high-dimensional data analysis, nonparametric regression, causal inference challenges, and model selection methods.
3) The key message is that econometrics can benefit from adopting techniques from fields like machine learning and statistics to develop more flexible, data-driven models.
Principles of Actuarial Science Chapter 3ssuser8226b2
1. The document discusses survival models and hazard rates used in actuarial science to calculate probabilities related to life insurance and annuity contracts. It covers survival functions, hazard rates, actuarial notation, and life tables.
2. A life table shows values like the probability of death between each age and expected remaining lifetime for each age based on mortality data. The document provides examples of constructing and using life tables.
3. Simple models for hazard rates over age include De Moivre's law and Gompertz and Makeham curves. These can be fitted to life table data using least squares to estimate parameters.
Efficient Numerical PDE Methods to Solve Calibration and Pricing Problems in ...Volatility
This document discusses efficient numerical PDE methods to solve calibration and pricing problems in local stochastic volatility models. It begins with an overview of volatility modelling, including local stochastic volatility models that combine local volatility, jumps, and stochastic volatility. It then discusses calibrating both parametric and non-parametric local volatility models using PDE methods. The document provides examples of modelling stochastic volatility factors using implied volatility data and estimating jump parameters from historical returns. It also discusses calibrating local volatility models to vanilla option prices while including jumps and stochastic volatility.
1. The document discusses methods for estimating and analyzing saetas (linear models). It proposes estimating a saeta under a new reference frame by applying the appropriate transformation to the estimated saeta coefficients.
2. Once a saeta is estimated, it can be restricted to pass through the origin by applying a linear restriction to the model estimation. The restriction can be tested with an F-test.
3. When two saetas are estimated from different data sets, the best overall saeta can be determined by testing whether the two saetas are equal.
Anomaly Detection in Sequences of Short Text Using Iterative Language ModelsCynthia Freeman
The document discusses various methods for anomaly detection in time series data. It begins by defining time series and anomalies, noting that anomaly detection is challenging due to issues like lack of labeled data and data imbalance. It then covers characteristics of time series like seasonality, trends, and concept drift, and how to detect them. Various anomaly detection methods are outlined, including STL, SARIMA, Prophet, Gaussian processes, and RNNs. Evaluation methods and factors to consider in choosing a detection method are also discussed. The document provides an overview of approaches to determining the optimal anomaly detection model for a given time series and application.
How Does CRISIL Evaluate Lenders in India for Credit RatingsShaheen Kumar
CRISIL evaluates lenders in India by analyzing financial performance, loan portfolio quality, risk management practices, capital adequacy, market position, and adherence to regulatory requirements. This comprehensive assessment ensures a thorough evaluation of creditworthiness and financial strength. Each criterion is meticulously examined to provide credible and reliable ratings.
Independent Study - College of Wooster Research (2023-2024) FDI, Culture, Glo...AntoniaOwensDetwiler
"Does Foreign Direct Investment Negatively Affect Preservation of Culture in the Global South? Case Studies in Thailand and Cambodia."
Do elements of globalization, such as Foreign Direct Investment (FDI), negatively affect the ability of countries in the Global South to preserve their culture? This research aims to answer this question by employing a cross-sectional comparative case study analysis utilizing methods of difference. Thailand and Cambodia are compared as they are in the same region and have a similar culture. The metric of difference between Thailand and Cambodia is their ability to preserve their culture. This ability is operationalized by their respective attitudes towards FDI; Thailand imposes stringent regulations and limitations on FDI while Cambodia does not hesitate to accept most FDI and imposes fewer limitations. The evidence from this study suggests that FDI from globally influential countries with high gross domestic products (GDPs) (e.g. China, U.S.) challenges the ability of countries with lower GDPs (e.g. Cambodia) to protect their culture. Furthermore, the ability, or lack thereof, of the receiving countries to protect their culture is amplified by the existence and implementation of restrictive FDI policies imposed by their governments.
My study abroad in Bali, Indonesia, inspired this research topic as I noticed how globalization is changing the culture of its people. I learned their language and way of life which helped me understand the beauty and importance of cultural preservation. I believe we could all benefit from learning new perspectives as they could help us ideate solutions to contemporary issues and empathize with others.
[4:55 p.m.] Bryan Oates
OJPs are becoming a critical resource for policy-makers and researchers who study the labour market. LMIC continues to work with Vicinity Jobs’ data on OJPs, which can be explored in our Canadian Job Trends Dashboard. Valuable insights have been gained through our analysis of OJP data, including LMIC research lead
Suzanne Spiteri’s recent report on improving the quality and accessibility of job postings to reduce employment barriers for neurodivergent people.
Decoding job postings: Improving accessibility for neurodivergent job seekers
Improving the quality and accessibility of job postings is one way to reduce employment barriers for neurodivergent people.
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1. Azerbaijan Republic
Khazar University
MBA THESIS
“Actuarial analysis in social security”
MBA Thesis Presentation for the Master Degree at Khazar University, on 14th December
School : Economics & Management
Student: Hikmet Tagiyev Sakhavet
Supervisor : Dr.Oktay Ibrahimov Vahib
Baku 2007
2. Research Objectives
Theoretical:
- To identify economic criteria for analyzing social security systems and
pension reform, in the context of population aging
Empirical:
- To quantify the effects of demography + pension systems + pension
reforms on future poverty + inequality, for aging countries
- To develop simulation tool for theory validation and policy making
3. Aging
• Population Aging = lower mortality + lower fertility + higher life
expectancy
• By 2050, in EU:
proportion of +65 projected to double
average projected increase in dependency ratios (Old /
Young, Pensioners / Workers) from 24% to 49%
average projected increase in retirement years
average projected increase in pension expenditure by 3-5 %
4. What Future ?
• Future welfare of pensioners will depend on complex interactions
between Demography + Labour + Pension System.
– Aging can affect sustainability / efficiency of a Pension
System
– Pension System can also induce behavioural changes e.g.
increased retirement age which can counterbalance
demographic effects
• Economic consequences of Aging and Pension System need to be
analysed together net effects.
• We need a model for net effects what pension system is better
to address consequences of aging?
5. Our Questions…
1. How much protection can be provided with a given level of financial
resources?
2. What financial resources are necessary to provide given level of
protection?
3. Who will be covered? (Legal versus actual coverage)
4. What kind of benefit will be provided? (Benefit provisions )
5. What part of workers’ earnings will be subject to contributions and
used to compute benefits? (This refers to the floor and ceiling of
earnings adopted for the scheme.
6. What should be the earnings replacement rate in computing benefits?
7. Should the scheme allow for cross-subsidization between income
groups through the benefit formula?
8. What will be the required period of contribution as regards eligibility
for the various benefits?
9. What is the normal retirement age?
10. How should benefits be indexed?
11. Who pays and how much ? (Financing provisions)
6. What is an Actuary?
Better Definitions
• “One who analyzes the current financial implications of
future contingent events”
• “Actuaries put a price tag on future risks. They have
been called financial architects and social
mathematicians, because their unique combination of
analytical and business skills is helping to solve a
growing variety of financial and social problems.”
7. The Actuarial Science
Research Triangle
Mathematics
Fuzzy Set Stochastic Calculus /
Theory Ito’s Lemma
Markov Chain Financial Mathematics
Monte Carlo Theory Interest
of Risk Theory
Chaos Theory /
Fractals
Dynamic Interest
Financial Rate
Actuarial Analysis Modeling
Finance
Science Portfolio Contingent
Theory Claims
Analysis
8. Principles and techniques of actuarial analysis
1 –The projection technique - The actuarial analysis starts with a
comparison of the scheme’s actual demographic and financial
experience against the projections.
2 –The present value technique - This technique considers one cohort
of insured persons at a time and computes the probable present values of
the future insured salaries, on the one hand and of the pension benefits
payable to the members of the cohort and to their survivors, on the other.
9. The demographic projection technique (1)
The first step in the projection technique is the demographic projections, production
of estimates of numbers of individuals in each of the principal population subgroups
(active insured persons -A(t), retirees-R(t), invalids-I(t), widows/widowers- W(t),
orphans –O(t) at discrete time-points (t=1,2,..),starting from given initial values (at t=0).
The demographic projection procedure can be regarded as the iteration of a matrix
multiplication operation, typified as follows :
nt = nt −1 ⋅ Qt −1
in which is a row vector whose elements represent the demographic projection values
at time t and is a square matrix of transition probabilities for the interval (t-1, t) which
take the form:
p (aa) q (ar) q (ai) q (aw) q (ao)
(rr)
0 p 0 q (rw) q (ro)
nt = [ A(t) R(t) I(t) W(t) O(t)] Qt = 0 0 p (ii) q (iw) q (io)
0 0 0 p (ww)
0
(oo)
0
0 0 0 p
10. The demographic projection technique (2)
The elements of the matrix and the symbols have the following significance:
p (aa) , p (rr) ,... denotes the probability of remaining in the same r;
q (ar) , q (ai) , q (aw) , q (ao) ,... denotes the probability of transition from status a to
status r, i, w, o ;
a, r , i , w and o respectively represent active lives , retirees, invalids,
widows/widowers and orphans .
11. The demographic projection technique (3)
For carrying out the demographic projections it is necessary to adopt an actuarial basis, consisting
of the elements listed below:
The active table : a
lx , b ≤ x ≤ r
where b is the youngest entry age and the r the highest retirement age. The associated dependent
a
rates of decrement are denoted by q x (mortality) and ix (invalidity). Retirement is assumed to take
place at exact integral ages, just before each birthday, rx denoting the proportion retiring at age x.
The following expressions for the age and sex – specific one year transition probabilities are based
on the rules of addition and multiplication of probabilities:
a) Active to active : p (aa) = (1 - q a - i x ) ⋅ (1 - rx +1 )
x x
b) Active to retiree q (ar) = (1 - q a - i x ) ⋅ rx +1
x x
c) Active to invalid q (ai) = (1 - 0,5 ⋅ q ix ) ⋅ i x
x
12. The demographic projection technique (4)
We can also analyze below tables:
• The life table for invalids lx , b ≤ x < D
i
• The life table for retired persons l xp , r ≤ x < D
• The table for widows/widowers l y , y* ≤ y ≤ D
w
• The table for orphans l zo , 0 ≤ z ≤ z *
where b is the youngest entry age ; r the highest retirement age; D the death
age; y* the lowest age of a widow /widower ; z* the age limit for orphans’
pensions
13. The demographic projection technique (5)
Starting from the population data on the date of the valuation (t=0), the transition probabilities are
applied to successive projections by sex and age. The projection formula for the active insured
populations are given below, the method of projecting the beneficiary populations is illustrated with
reference retirement pensioners.
• Act(x, s, t) – denotes the active population aged x nearest birthday , with curtate past service duration s
years at time t ;
• Ac(x, t),Re(x, t) –denotes the active and beneficiary population aged x nearest birthday at
time t
• A(t), R(t) – denotes the total active and beneficiary population at time t
The projection of the total active and beneficiary populations from time t-1 to time t is expressed by
the equation:
r
A(t ) = ∑∑ Act ( x, s, t ) + Act ( x-1,s-1,t-1) ⋅ ( p (aa) − q xar ) − q xai ) − q xaw) − q x )
x-1
( ( ( a
x =b s > 0
D
R (t ) = ∑ Ac(x − 1,t − 1) ⋅ q (ar) + Re(x − 1,t − 1) ⋅ (p (rr) − q x )
x −1 x −1
r
x=r
14. The financial projection technique (1)
The basis for the financial projections would comprise assumptions in regard to
the following elements. They are specified as functions of age or time, the age
related elements should be understood to be sex specific and may be further
varied over time, if necessary.
• ss(x,t) : The age –related salary scale function aged x at time t
• b(x,t) : The factor average per capita pension amount of the pensioners aged
x at time t
• γt: The rate of salary escalation (increase) in each projection year
• β : The rate of pension indexation in each projection year
t
• dc(x) : The contribution density, that is, the fraction of the year during which
contributions are effectively payable
15. The financial projection technique (2)
The average salary at age x in projection year t is then computed by the formula
∑ ∑ Ac(y,t)
r −1 r −1
s(y,t −1) ⋅ Ac(y,t −1)
s(x,t) = ss(x,t) ⋅(1 +γ ) ⋅ b
⋅ b
∑ ∑ Ac(y,t −1)
t r −1 r −1
b
ss(y,t) ⋅ Ac(y,t) b
The total insured salary bill at time t would be estimated as:
S (t ) = ∑ Ac( x, t ) ⋅ s ( x, t ) ⋅ dc( x)
x
The total pension amount at time t would be estimated as:
P (t ) = ∑ Re( x, t ) ⋅ b( x − 1, t − 1) ⋅ (1 + β t )
x
where Ac(x,t) and Re(x,t) denotes the projected active and beneficiary population
aged x at time t.
16. The present value technique
• This technique considers one cohort of insured persons at a time and computes
the probable present values of the future insured salaries, on the one hand and of
the pension benefits payable to the members of the cohort and to their survivors,
on the other.
• The present value formulae will be developed for the simple case where the
pension accrues at 1percent of the final salary per year of service.
• A series (sex-specific) special commutation functions are needed for applying
the present value technique. Functions based on the Life table will be computed
at interest rate i, while those based on the other tables will be computed at rate j.
• A life table is a mathematical construction that shows the number of people
alive (based on the assumptions used to build the table) at a given age, or other
probabilities associated with such a construct.
17. Life Table based actuarial calculations
i = 12%
Age(x) lx qx px dx Vx Dx Nx Sx Cx Mx äx Ax
1/(1+i)x x
V * lx DX NX
x+1
V * dx CX Nx/Dx Mx/Dx
0 100 000 0,028500 0,971500 2 850 1,000000 100000,0 582 185,56 3 462 212,27 2 375,00 2 969,07 5,82 0,05
1 97 150 0,002386 0,997614 232 0,833333 80958,3 482 185,56 2 880 026,71 160,99 594,07 5,96 0,03
2 96 918 0,002386 0,997614 231 0,694444 67304,3 401 227,22 2 397 841,15 133,84 433,08 5,96 0,02
18 95 755 0,000619 0,999381 59 0,037561 3596,7 21 469,75 127 772,27 1,85 18,37 5,97 0,05
19 95 696 0,000689 0,999311 66 0,031301 2995,4 17 873,09 106 302,52 1,72 16,52 5,97 0,05
20 95 630 0,000759 0,999241 73 0,026084 2494,4 14 877,72 88 429,44 1,58 14,80 5,96 0,06
60 78 273 0,018944 0,981056 1 483 0,000018 1,4 7,34 37,16 0,02 0,17 5,28 0,82
99 940,2 0,288432 0,711568 271 0,000000 0,0 0,00 0,01 0,00 0,00 66,84 76,43
100 669 1,000000 0,000000 669 0,000000 0,0 0,00 0,01 0,00 0,00 113,71 149,49
: is the number of people alive, relative to an original cohort, at age x.
: shows the number of people who die between age x and age x + 1
: is the probability of death between the ages of x and age x + 1.
: is the probability of a life age x surviving to age x + 1.
: is a discount factor used to obtain the amount of money that must be
invested now in order to have a given amount of money in the future. For example if
you need 1 in one year then the amount of money you need now is: If you need
25 in 5 years the amount of money you need now is:
18. Life Table based actuarial calculations
i = 12%
Age(x) lx qx px dx Vx Dx Nx Sx Cx Mx äx Ax
1/(1+i)x x
V * lx DX NX
x+1
V * dx CX Nx/Dx Mx/Dx
0 100 000 0,028500 0,971500 2 850 1,000000 100000,0 582 185,56 3 462 212,27 2 375,00 2 969,07 5,82 0,05
1 97 150 0,002386 0,997614 232 0,833333 80958,3 482 185,56 2 880 026,71 160,99 594,07 5,96 0,03
2 96 918 0,002386 0,997614 231 0,694444 67304,3 401 227,22 2 397 841,15 133,84 433,08 5,96 0,02
18 95 755 0,000619 0,999381 59 0,037561 3596,7 21 469,75 127 772,27 1,85 18,37 5,97 0,05
19 95 696 0,000689 0,999311 66 0,031301 2995,4 17 873,09 106 302,52 1,72 16,52 5,97 0,05
20 95 630 0,000759 0,999241 73 0,026084 2494,4 14 877,72 88 429,44 1,58 14,80 5,96 0,06
60 78 273 0,018944 0,981056 1 483 0,000018 1,4 7,34 37,16 0,02 0,17 5,28 0,82
99 940,2 0,288432 0,711568 271 0,000000 0,0 0,00 0,01 0,00 0,00 66,84 76,43
100 669 1,000000 0,000000 669 0,000000 0,0 0,00 0,01 0,00 0,00 113,71 149,49
Special commutation functions based on the active and retirees table
D x = x ⋅v x
a
la Dxp = l xp ⋅ v x
∑
D
D x =D x ⋅s x
as a
− p Dtp + Dtp 1
+
Nx = t =r
− as D as
+ D as
− p
2
Dx = x x+ 1
− p
2 Nx
− as r−1 − ax =
D xp
N x =∑D
t=x
t
as
where b is the youngest entry age ; r the highest retirement age;sx the age related
salary scale function; .. indicates a life insurance benefit of 1 payable at the end
of the year of death; a x indicates an annuity of 1 unit per year payable at the start of
each year until death to someone currently age x .
19. Present values of insured salaries and benefits
• Present value of insured salaries ( b ≤ x < r )
− as − as
N x −N r
PVS(x) = as
Dx
• Present value of retirement pensions
Dras _p
PVR(x) = p (r , x) as a r
Dx
where p (r, x) denotes the retirement pension of the cohort aged x as a
proportion of the final salary.
20. Macro-economic parameters in
actuarial calculations
The economic variables necessary to develop a suitable macroeconomic frame include :
• economic growth
• the separation of GDP between remuneration of workers and broadly, remuneration of
capital
• labour force, employment and unemployment
• wages
• inflation
• bank (interest) rate
• taxes and other consideritions.
21. The general frame for macroeconomic projections
Fertility
Initial general Projected general
Mortality
population population
Migration
Initial labor Future evaluation of Projected labor
force the participation rate force
Projected active Projected inactive
population population
Future evaluation
of GDP
Historical
•GDP Projected Projected
•Employment employment unemployment
•productivity
Future productivity
Source: International Labor Organization (2002).
22. Macro-economic parameters in
actuarial calculations
The financial projections of a social security scheme depend on:
• the number of people who will pay contributions to the scheme ;
• the average earnings of these contributors ;
• the number of people who will receive benefits;
• the amount of benefits that will be paid, related to past earnings and
possibly indexed;
• the investment earnings on the reserve.
23. Determination of the average wage in the economy
Labor force supply model
(projected active population)
Historical
•GDP
•Employment Future productivity
•productivity
Projected Projected
employment unemployment
Future evaluation
of GDP
Historical share
of wages in GDP
Projected total Projected
remuneration Average wage
Projected share
of wages in GDP
Historical total
remuneration
Source: International Labor Organization (2002).
Wage distribution assumptions are needed to simulate the possible impact of the social
protection system on the distribution of income, for example, through minimum and maximum
pension provisions.
Assumptions on the differentiation of wages by age and sex must then be established, as
well as assumptions on the dispersion of wages between income groups.
24. Types of Pension Systems
• Pension Pillars = Public + Private
• Each Pillar can vary in:
– Type of Benefit: Defined Benefit vs. Defined Contribution
– Degree of Actuarial Fairness: Non-Actuarial (DB) vs. Actuarial (DC)
– Type of Financing: Funded vs. Unfunded (Pay-as-you-go)
• A Pension System consists of a given combination along these 3 dimensions
• Pension Reform usually entails moving along any of these dimensions.
• Parametric Reforms:
– Changes to retirement age, replacement ratio (avg.pension/avg.wage), contribution
rate, indexing
• Systemic Reforms:
– Changes to system structure or financing of the system
• Moving to Funding
• Making benefit more actuarial (DC)
• “Multi-Pillar” Model (World Bank):
– 1st: Minimum State Pension (flat)
– 2nd: Mandatory Occupational Pension (funded)
– 3rd: Voluntary Private Pension Savings
25. Rate of Return and Internal Rate of Return
• Rate of return (ROR) comprises the proportional difference of what participant pay
as contribution and the amount he gets as pension. In this research we get the
following formula:
RORG+,1 = λt + ρt + λt ⋅ ρt = λt + ρt
t
A
Neglible
where ρ t : The growth rate of working generation. λt : Wage growth rate.
• Internal rate of return (IRR) is one of the most important money measures for
pension schemes promises and contracts. IRR is the rate that makes the present value
of future promised benefits equal to the present value of all injected contributions in
the system. Mathematically speaking, IRR is the discount rate (r) that solves the
following equation: LE
Bt RA
Crm ⋅ Ym
∑+1 (1 + r )t = m∑ (1 + r )m
t = RA = EA
t m
where Bt is the value of benefits at age t, RA represents the age at which the person retires,
LE life expectancy at the age of retirement, Crm: the contribution rate at age m, r: the discount
rate, Y is the level of income on which the contribution is based on and EA is the age at which
m
the pensioner starts his career.
26. The framework
Basic Inputs by year Base Line assumptions
Types of pension schemes
Impact of
• Population growth
• Interest rate
Pension Reform Illustrated Different scenarios
•Decline in fertility rate
Simulation Model (PRISM) #1, #2, #3, …..
•Increase in longevity
•Change in employment rates
•Increase in retirement age
Repeat it “lot of times”
With & Without the rule Aggregate sums, counts,
Contributions
Pension benefits (Average Gain & IRR)
Balance Ratio (assets & liabilities)
Analyse
& make your choice
Ready!
27. An Overview of the PRISM Model
• This model is a tool for illustrating the basic principles of pension-
system finance. The model is "stylized" -- it is not a model of a real
pension system, but rather a model of a very simple fictitious pension
system.
• The model can simulate defined benefit systems, defined contribution
systems, pay-as-you-go systems, capitalized systems, partially
capitalized systems, and mixed systems (defined benefit and defined
contribution).
• In this system, all individuals enter the labor market at age 20, work
continuously through age 59, retire at age 60, and die on their 80th
birthday.
• The system is launched in the year 1920. Thus, in 1920, only persons
who are 20 years old make contributions to the system. In 1960, the
first pensioners appear, retiring on their 60th birthday. In 1980, the first
cohort of pensioners reaches age 80, and they die. Thus, the system
requires 60 years to reach maturity.
28. Scenario 1.The impact of population growth on PAYG(DB) system
• Assume:
– promised benefit (RR) = 40% wage
– Contribution rate (CR) =10% wage .
– Population growth rate is 0%.
//The key mathematic idea is "internal-rate-of-return". The IRR is the interest rate
that equalizes the present value of a person's contributions with the present
value of their pensions. The sustainable IRR of a PAYG plan is equal to wage
growth (w) plus population growth (e).
• In this case, the IRR is 2.3% greater than wage growth. To sustain this
promised IRR, either population growth must be above a particular threshold.
Why?
• The IRR promised to participants is equal to wage growth plus 2.3%, and the
IRR that the system can afford to pay is equal to wage growth plus population
growth. Thus, population growth must be at least 2.3%.
29. Scenario 2.How is PAYG(DB) system affected by a decline in fertility rate
• Assume:
– promised benefit (RR) = 40% wage
– Contribution rate (CR) =10% wage .
– Population growth rate is 2.3%, but in 1990we assume that we assume that
birth rates decline such that the number of babies born each year remains
constant, rather than increasing at a rate of 2.3%.This change in birth rates
causes the entire population to stabilize such that it is neither growing.
• In this case, the IRR is 2.3% greater than wage growth. To sustain this
promised IRR, either population growth must be above a particular threshold.
Why?
• Begin by examining the ratio of the population above the age of 60 to the
population of ages 20 to 59 .Initially, this ratio is 25%, but beginning in the
year 2010 (20 years after the decrease of fertility rates), this ratio begins to
increase. By the year 2065, the ratio has increased to 50%. This dramatic
demographic change has a profound impact on the operation of the pension
system.
• Due to the demographic changes, a large deficit emerges in the long run:
contributions are merely 10% of wage bill, while expenditures are 20% of wage
30. Scenario 3.How is Funded system affected by a decline in fertility rate
• Assume:
– promised benefit (RR) = 40% wage
– Contribution rate (CR) =10% wage .
– Population growth rate is 2.3%, but in 1990we assume that we assume that
birth rates decline such that the number of babies born each year remains
constant, rather than increasing at a rate of 2.3%.This change in birth rates
causes the entire population to stabilize such that it is neither growing.
• Despite this dramatic demographic change, the pension system remains stable
throughout the simulation. This is clearly evident if we examine the ratio of the
system's assets to liabilities.
• This ratio remains constant at 100% throughout the simulation, implying that
the system is always fully funded, despite the demographic changes. How is
this possible?
• It is possible because we have assumed that the interest rate earned on the
system's assets is 2.3% -- precisely equal to the IRR that the system promises to its
participants. Therefore, growth of the system's assets will keep pace with growth
of the system's liabilities, regardless of changes in fertility rates.
31. Scenario 4.How is PAYG DB and Funded affected by an increase in longevity
• Assume:
– promised benefit (RR) = 40% wage
– Contribution rate (CR) =10% wage .
– Population growth rate is 2.3%, but in 1990 and 2030 we gradually increase
the post-retirement lifetime from 20 years to 24 years.
•The results are not surprising: deficits emerge as the post-retirement lifetime
increases, because pensions must be paid over a longer period.
• But in Funded system, when we increase longevity, participants receive
pension benefits for a longer period, which means the IRR promised to each
individual participant must increase. It is no longer 2.3%. Rather, the promised
IRR has increased to 2.7%.
• But the interest rate earned on the system's assets remains 2.3%. Therefore, the
system's assets are slowly depleted over time, because asset growth does not
keep pace with liability growth. In 2227, all assets will be depleted.
32. Scenario 4.How is PAYG DB affected by a retirement age increase
• Assume:
– promised benefit (RR) = 44% wage
– Contribution rate (CR) =10% wage .
– Population growth rate is 0%
• When considering the long-range effects of a retirement age will the retirement age change lead
to an increase or a decrease of the promised IRR?
• On the one hand, the retirement age increase will shorten the period over which individuals
receive their pensions, which will have a downward effect on the promised IRR.
•On the other hand, the retirement age change may lead to an increase in replacement rates, which
will have an upward effect on the promised IRR. The net effect of these two opposing forces will
depend, to a large extent, on the design of the benefit formula.
• Given these parameters, the promised IRR is equal to wage growth plus 0.3%. This means that
the system requires population growth of 0.3% per year to ensure long run balance between
contributions and expenditures. However, we have assumed population growth of 0%, and, as a
consequence, the system runs small deficits: contributions are equal to 20% of wage bill,
expenditures are equal to 22%, and the deficit is equal to 2% of wage bill.
• To eliminate these deficits, the Government raises the retirement age from 60 to 63. This
increases the replacement rate (because people work longer), but decreases the average period over
which people receive pensions. The net effect is to reduce the promised IRR from wage growth
plus 0.3% to wage growth minus 0.2%. Because population growth is greater than -0.2%, the
system runs small surpluses
34. Some actuarial calculations with regards to the Turkish pension system
(Calculation of the value of the accrued liabilities)
Assumptions male/female by age
1. Investment income (Inv) – 12%
2. Inflation rate (Inf.) - 0%
3- Technical rate of interest = (1+Inv)/ (1+inf.) -1
4- Survivor’s benefit: This liability is assumed to be a percentage of the liability for old age pension – 30%
Mortality table used for males and females (All rates are per 1000 lives)
Male Female
Age l(x) q(x) D(x) N(x) Age q(y) l(y) D(y) N(y)
20 99690 0,00170 99 690 299 540 20 0,00080 99 181 99 181 598 221
30 97843 0,00190 97 843 1 286 520 30 0,00120 98 207 98 207 2 571 677
40 95121 0,00330 95 121 2 251 294 40 0,00210 96 507 96 507 4 519 082
50 89443 0,00860 89 443 3 175 285 50 0,00480 92 950 92 950 6 414 988
55 83782 0,01390 83 782 3 606 541 55 0,00710 89 731 89 731 7 326 084
60 75150 0,02140 75 150 4 001 105 60 0,01150 84 948 84 948 8 196 467
65 63040 0,03280 63 040 4 341 912 65 0,01950 76 969 76 969 9 001 054
70 47310 0,05250 47 310 4 610 079 70 0,03490 65 768 65 768 9 707 327
80 16628 0,13010 16 628 4 906 129 80 0,10250 30 327 30 327 10 647 942
90 2003,4 0,27420 2 003 4 976 374 90 0,25040 4 941 4 941 10 936 890
100 0,0576 1,00000 0 4 980 095 100 1,00000 0 0 10 956 655
35. Present value factors and Total actuarial liability
• Present value factors are calculated on the basis of the assumptions per unit of annual benefit.
Active Pensioner
Age Male Female Age Male Female
PV factor
Ret.Age (Nx/Dx) Ret. Age PV factor PV factor PV factor
20 57 0,84 55 1,20 20 15,25 15,56
30 52 2,59 49 3,74 30 14,61 15,04
40 47 7,70 48 7,73 40 13,48 14,16
50 53 8,97 57 7,00 50 11,76 12,75
60 70 2,66 68 4,43 60 9,56 10,63
65 74 2,15 74 2,82 65 8,29 9,30
70 80 1,05 81 1,20 70 6,97 7,85
80 80 4,71 92 0,10 80 4,71 5,26
90 90 2,62 92 1,04 90 2,62 2,74
100 100 100
• Liabilities are calculated on the basis of the present value factors and the total pension (old age, mortality,
survivors) amount by sex and age. If the interest rate increases, then total liability will be decrease.
TOTAL LIABILITY PER 31-12-2001 IN TL 1.000.000
Technıcal ınterest rate 0% % 6% % 12% %
Actıve insureds 346 030 144 765 69% 65 450 816 224 89% 28 686 362 148 84%
Pensioners 152 573 772 622 31% 7 732 068 204 11% 5 278 595 965 16%
TOTAL 498 603 917 387 100% 73 182 884 429 100% 33 964 958 112 100%
36. Aging in Azerbaijan
Currently, Azerbaijan’s population is nearly 8, 5 million. . As UN projection
model finds, total population would increase up to approximately 10, 5 million
in 2050.
The total fertility rate dropped from 2.6 in 1990 to a low point of
1.8 in 2006. But it will be increase up to approximately 1, 94 in 2050.
Azerbaijan is young: + 60 “only” 10.5%. But…Proportion of +60
projected to be 32.1 % in 2050
Dependency ratio (+60/15-59) will increase from 17.3% to 42.9%
end of 2050.
The dependency ratio will be effect after 2015 year
38. Expected life expectancy
90
81,27 81,77
80 77,07 77,87 78,37 79,17 79,97 80,77
75,47 76,27 74,91 75,71 76,21
74,47 73,31 74,11
71,51 72,31
70 67,21 68,71 69,71 70,71
60
50
40
30 26,3 26,7 27 27,2
24,2 24,5 24,9 25,2 25,5 25,9
23,8 22,2
22,3 22,6 23
22,8 23,1
23,2
21,3 21,5 21,9
20 20,1
19,7
16,7
20,4
20,2
17,1
20,7
20,5
17,3
21
20,9
17,6
21,2
17,9 18,1 18,5 18,8 19 19,4 19,6
10
0
2000 2005 2010 2015 2020 2025 2030 2035 2040 2045 2050
Male at birth Female at birth Male at age 60
Female at age 60 Male at age 65 Female at age 65
2000 2005 2010 2015 2020 2025 2030 2035 2040 2045 2050
At birth 67,21 68,71 69,71 70,71 71,51 72,31 73,31 74,11 74,91 75,71 76,21
Male at age 60 19,7 20,2 20,5 20,9 21,2 21,5 21,9 22,3 22,6 23,0 23,2
at age 65 16,7 17,1 17,3 17,6 17,9 18,1 18,5 18,8 19,0 19,4 19,6
At birth 74,47 75,47 76,27 77,07 77,87 78,37 79,17 79,97 80,77 81,27 81,77
Female at age 60 23,8 24,2 24,5 24,9 25,2 25,5 25,9 26,3 26,7 27,0 27,2
at age 65 20,1 20,4 20,7 21,0 21,3 21,5 21,9 22,2 22,6 22,8 23,1
39. Conclusion
The study is devoted to the mechanisms of the actuarial analysis being applied in various
countries.
• EU model (PRISM) and ILO pension model were used for the simulations. However almost all of the
demographic and economic assumptions were updated based on UN’s statistical data.
• A number of different actuarial calculations have been done on the effects of population ageing .
Management of the economic and social consequences of population ageing will require three mutually supportive
elements.
1. The volumes needed for financing pensions mean the system will always have to be based on a public pay-
as-you-go scheme.
2. In top of this there will also be a need for a solid funded element to balance out disturbances, spread
the burden between generations and thus help the economy adapt to the demographic changes.
3. As a third pillar , we will also need to provide a clear framework for private pension savings that will
provide scope for personal planning and fill any gaps that remain in the public system.
• Finally, consideration should be given as to whether there should be greater integration of demographic and
economic assumptions; in other words, should greater consideration be given to their interdependencies since, in
the long term at least, the demographic situation of a country is closely linked to its economic situation.