This document discusses using R packages to model and simulate annuities while accounting for variability and uncertainty. It introduces the lifecontingencies package for actuarial calculations and describes collecting demographic and financial data. Baseline assumptions are defined and the Lee-Carter model is used to project mortality. Variability is assessed through simulating process variance in lifetimes and annuity present values, and parameter variance by generating random life tables. Interest rates are modeled with Vasicek dynamics and inflation is linked to interest rates through cointegration. The overall algorithm simulates annuity distributions by projecting cash flows over simulated lifetimes and interest/inflation rates.
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 discusses using the markovchain package in R to model and analyze long-term care (LTC) insurance policies. It presents transition probabilities for disabled, ill, and dead states for Italian males. The package is used to simulate life trajectories and cash flows to calculate policy premiums and reserves. Simulation allows for stochastic analysis of benefits and reserves over many simulated policyholder lives.
The document presents the results of creating and back-testing a factor-based long-short global tactical asset allocation strategy using 10 years of monthly data on 10 developed country equity index futures. Three 2-factor portfolios were constructed using value, momentum, and volatility factors. The portfolio combining value and volatility factors performed best with an annualized return of 7.24% and average drawdown of 13.01%.
Colleen P Cahill Econometrics Work Examplecolleenpcahill
This document estimates several linear probability models to predict the outcome of US presidential elections from 1972 to 1992. It finds that only the coefficient on the incumbent party's candidate's vote share is statistically significant. When predicting the 1996 election, the model correctly predicts that Clinton would win. Testing finds no evidence of serial correlation in the errors. Using robust standard errors does not substantially change the significance of any variables.
Risk-Aversion, Risk-Premium and Utility TheoryAshwin Rao
This lecture helps understand the concepts of Risk-Aversion and Risk-Premium viewed from the lens of Utility Theory. These are foundational economic concepts used widely in Financial applications - Portfolio problems and Pricing problems, to name a couple.
Affine Term Structure Model with Stochastic Market Price of RiskSwati Mital
- The document proposes a new affine term structure model that combines principal components analysis with a stochastic market price of risk.
- Principal components provide useful information about yield curves and only three components explain over 95% of yield variation.
- Previous models linked risk premium deterministically to return-predicting factors like slope, but this could result in unrealistic risk premium levels.
- The new model introduces an additional state variable to capture the stochastic market price of risk and break the deterministic link between risk premium and return-predicting factors.
The document discusses quantifying uncertainty in claims reserving over a one year horizon, as required by Solvency II. It formalizes the claims reserving problem and describes how actuaries must predict total payments for each accident year based on available information. Chain ladder modeling is presented as a standard approach to estimate development factors and project future payments. The document proposes a proposition relating cumulative payments to development factors estimated from the chain ladder model.
The Artful Business of Data Mining: Computational Statistics with Open Source...David Coallier
This talk goes over a concepts of data mining and data analysis using open source tools, mainly Python and R with interesting libraries and the tools I have used and currently use at Engine Yard.
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 discusses using the markovchain package in R to model and analyze long-term care (LTC) insurance policies. It presents transition probabilities for disabled, ill, and dead states for Italian males. The package is used to simulate life trajectories and cash flows to calculate policy premiums and reserves. Simulation allows for stochastic analysis of benefits and reserves over many simulated policyholder lives.
The document presents the results of creating and back-testing a factor-based long-short global tactical asset allocation strategy using 10 years of monthly data on 10 developed country equity index futures. Three 2-factor portfolios were constructed using value, momentum, and volatility factors. The portfolio combining value and volatility factors performed best with an annualized return of 7.24% and average drawdown of 13.01%.
Colleen P Cahill Econometrics Work Examplecolleenpcahill
This document estimates several linear probability models to predict the outcome of US presidential elections from 1972 to 1992. It finds that only the coefficient on the incumbent party's candidate's vote share is statistically significant. When predicting the 1996 election, the model correctly predicts that Clinton would win. Testing finds no evidence of serial correlation in the errors. Using robust standard errors does not substantially change the significance of any variables.
Risk-Aversion, Risk-Premium and Utility TheoryAshwin Rao
This lecture helps understand the concepts of Risk-Aversion and Risk-Premium viewed from the lens of Utility Theory. These are foundational economic concepts used widely in Financial applications - Portfolio problems and Pricing problems, to name a couple.
Affine Term Structure Model with Stochastic Market Price of RiskSwati Mital
- The document proposes a new affine term structure model that combines principal components analysis with a stochastic market price of risk.
- Principal components provide useful information about yield curves and only three components explain over 95% of yield variation.
- Previous models linked risk premium deterministically to return-predicting factors like slope, but this could result in unrealistic risk premium levels.
- The new model introduces an additional state variable to capture the stochastic market price of risk and break the deterministic link between risk premium and return-predicting factors.
The document discusses quantifying uncertainty in claims reserving over a one year horizon, as required by Solvency II. It formalizes the claims reserving problem and describes how actuaries must predict total payments for each accident year based on available information. Chain ladder modeling is presented as a standard approach to estimate development factors and project future payments. The document proposes a proposition relating cumulative payments to development factors estimated from the chain ladder model.
The Artful Business of Data Mining: Computational Statistics with Open Source...David Coallier
This talk goes over a concepts of data mining and data analysis using open source tools, mainly Python and R with interesting libraries and the tools I have used and currently use at Engine Yard.
Using Grammatical Evolution to develop trading rulesmy_slides_
This document describes using Grammatical Evolution to automatically generate trading rules based on a Backus-Naur Form (BNF) grammar. The best rules found after 100 generations are presented, which were profitable when backtested on historical S&P 500 data from 2000-2008. However, this test does not guarantee real-world performance, as commission costs and true forecasting were not considered. Further experiments are needed using a more complex grammar and realistic settings.
- The document provides an agenda for a presentation on mining trading strategies with R using quantstrat and R packages.
- It includes quick surveys of the audience, an overview of the architecture of a trading system, hands-on sessions on quantmod, PerformanceAnalytics, blotter and quantstrat, and discussions of basic concepts in quantitative trading and machine learning applications.
- The presenter is George Chang from Taiwan and organizes the Taiwan R User Group and MLDM Monday for applying machine learning in the real world through hands-on practice.
This document provides an overview of using R for financial modeling. It covers basic R commands for calculations, vectors, matrices, lists, data frames, and importing/exporting data. Graphical functions like plots, bar plots, pie charts, and boxplots are demonstrated. Advanced topics discussed include distributions, parameter estimation, correlations, linear and nonlinear regression, technical analysis packages, and practical exercises involving financial data analysis and modeling.
R in finance: Introduction to R and Its Applications in FinanceLiang C. Zhang (張良丞)
This presentation is designed for experts in Finance but not familiar with R. I use some Finance applications (data mining, technical trading, and performance analysis) that you are probably most familiar with. In this short one-hour event, I focus on the "using R" rather than the Finance examples. Therefore, few interpretations of these examples will be provided. Instead, I would like you to use your field of knowledge to help yourself and hope that you can extend what you learn to other finance R packages.
This document discusses using hidden Markov models (HMM) for stock price prediction. HMMs can model time series data as a probabilistic finite state machine. The document explains that HMMs can handle new stock market data robustly and efficiently predict similar price patterns to past data. It provides an overview of HMM components like states, transition probabilities, and emission probabilities. The document also demonstrates building an HMM model on stock data using the RHMM package in R, including training the model with Baum-Welch and predicting state sequences with Viterbi.
This document proposes improvements to existing customer lifetime value models. It discusses deriving current models A and B, which discount average revenues over a subscriber's expected duration. The improvements consider estimating future cash flows and growth rates through regression analysis, accounting for other revenue streams, and incorporating the value of a subscriber's social network. The proposed model uses discounted cash flow analysis and least squares regression to forecast revenues and growth rates for each subscriber, considering revenues from mobile, TV, broadband and the revenues of subscribers within their social network. It requires subscriber revenue and call data to implement the analysis.
This document discusses building regression and classification models in R, including linear regression, generalized linear models, and decision trees. It provides examples of building each type of model using various R packages and datasets. Linear regression is used to predict CPI data. Generalized linear models and decision trees are built to predict body fat percentage. Decision trees are also built on the iris dataset to classify flower species.
This document discusses quantitative forecasting methods, including time series and causal models. It covers key time series components like trend, seasonality, and cycles. Three main time series methods are described: smoothing, trend projection, and trend projection adjusted for seasonal influence. Moving averages and exponential smoothing are explained as common techniques for forecasting stationary time series. The document also covers decomposing a time series into trend, seasonal, and irregular components. Regression methods are mentioned as another approach when a trend is present in the data.
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.
This talk builds on recent empirical work addressing the extent to which the transaction graph serves as an early-warning indicator for large financial losses. By identifying certain sub-graphs ('chainlets') with causal effect on price movements, we demonstrate the impact of extreme transaction graph activity on the intraday volatility of the Bitcoin prices series. In particular, we infer the loss distributions conditional on extreme chainlet activity. Armed with this empirical representation, we propose a modeling approach to explore conditions under which the market is stabilized by transaction graph aware agents.
CVA In Presence Of Wrong Way Risk and Early Exercise - Chiara Annicchiarico, ...Michele Beretta
We will show how to calibrate the main parameter of the model and how we have used it in order to evaluate the CVA and the CVAW of a one derivative portfolio with the possibility of early exercise.
IRJET - Candle Stick Chart for Stock Market PredictionIRJET Journal
This document discusses using candlestick charts for stock market prediction. It begins with an introduction to how computers can now process large amounts of stock data using data mining techniques. It then provides background on candlestick formations and some common patterns. The methodology section outlines the process of collecting historical stock data on open, high, low, and close prices to generate candlestick charts. These charts can be analyzed for patterns to predict future stock price movements. Related work discusses how candlestick patterns have been shown to outperform methods based only on price changes. The conclusion is that this candlestick chart approach may enable more accurate short-term stock price forecasts compared to other methods.
This paper analyzes the swap rates issued by the China Inter-bank Offered Rate(CHIBOR) and
selects the one-year FR007 daily data from January 1st, 2019 to June 30th, 2019 as a sample. To fit the data,
we conduct Monte Carlo simulation with several typical continuous short-term swap rate models such as the
Merton model, the Vasicek model, the CIR model, etc. These models contain both linear forms and nonlinear
forms and each has both drift terms and diffusion terms. After empirical analysis, we obtain the parameter
values in Euler-Maruyama scheme and relevant statistical characteristics of each model. The results show that
most of the short-term swap rate models can fit the swap rates and reflect the change of trend, while the CKLSO
model performs best.
This is a pretty broad exploration and tutorial of basic econometrics modeling techniques. It includes an introduction to quite a few multiple regression methods. It also includes an extensive coverage of model testing to ensure that your model is quantitatively sound and statistically robust using state of the art peer reviewing protocol.
Affine cascade models for term structure dynamics of sovereign yield curvesLAURAMICHAELA
Rafael Serrano profesor de la Universidad del Rosario
Resumen:
In the first part of the talk, I will present an introduction to stochastic affine short rate models for term structure of yield curves In the second part, I will focus on a recursive affine cascade with persistent factors for which the number of parameters, under specifications, is invariant to the size of the state space and converges to a stochastic limit as the number of factors goes to infinity. The cascade construction thereby overcomes dimensionality difficulties associated with general affine models. We contrast two specfifications of the model using linear Kalman filter for a panel of Colombian sovereign yields.
Solution manual for essentials of business analytics 1st editorvados ji
Full download link :
https://getbooksolutions.com/download/solution-manual-for-essentials-of-business-analytics-1st-edition/
Detail about Essentials of Business : (Click link bellow to view example )
https://getbooksolutions.com/wp-content/uploads/2016/11/Solution-Manual-for-Essentials-of-Business-Analytics-1st-editor.pdf
Table of Contents
Chapter 1. What Is Business Analytics?
Chapter 2. Descriptive Statistics.
Chapter 3. Data Visualization.
4. Linear Regression.
5. Time Series Analysis and Forecasting.
6. Data Mining.
7. Spreadsheet Models.
8. Linear Optimization Models.
9. Integer Linear Optimization.
10. Nonlinear Optimization Models.
11. Monte Carlo Simulation.
12. Decision Analysis.
Monte Carlo Simulations (UC Berkeley School of Information; July 11, 2019)Ivan Corneillet
My guest lecture on Monte Carlo simulations [or "how to be approximately right, now vs. precisely wrong, later (or never…)"] for the Managing Cyber Risk course of UC Berkeley School of Information's Cybersecurity Master.
Achieving Consistent Modeling Of VIX and Equities DerivativesVolatility
1) Discuss model complexity and calibration
2) Emphasize intuitive and robust calibration of sophisticated volatility models avoiding non-linear calibrations
3) Present local stochastic volatility models with jumps to achieve joint calibration to VIX options and (short-term) S&P500 options
4) Present two factor stochastic volatility model to fit both the short-term and long-term S&P500 option skews
Using Grammatical Evolution to develop trading rulesmy_slides_
This document describes using Grammatical Evolution to automatically generate trading rules based on a Backus-Naur Form (BNF) grammar. The best rules found after 100 generations are presented, which were profitable when backtested on historical S&P 500 data from 2000-2008. However, this test does not guarantee real-world performance, as commission costs and true forecasting were not considered. Further experiments are needed using a more complex grammar and realistic settings.
- The document provides an agenda for a presentation on mining trading strategies with R using quantstrat and R packages.
- It includes quick surveys of the audience, an overview of the architecture of a trading system, hands-on sessions on quantmod, PerformanceAnalytics, blotter and quantstrat, and discussions of basic concepts in quantitative trading and machine learning applications.
- The presenter is George Chang from Taiwan and organizes the Taiwan R User Group and MLDM Monday for applying machine learning in the real world through hands-on practice.
This document provides an overview of using R for financial modeling. It covers basic R commands for calculations, vectors, matrices, lists, data frames, and importing/exporting data. Graphical functions like plots, bar plots, pie charts, and boxplots are demonstrated. Advanced topics discussed include distributions, parameter estimation, correlations, linear and nonlinear regression, technical analysis packages, and practical exercises involving financial data analysis and modeling.
R in finance: Introduction to R and Its Applications in FinanceLiang C. Zhang (張良丞)
This presentation is designed for experts in Finance but not familiar with R. I use some Finance applications (data mining, technical trading, and performance analysis) that you are probably most familiar with. In this short one-hour event, I focus on the "using R" rather than the Finance examples. Therefore, few interpretations of these examples will be provided. Instead, I would like you to use your field of knowledge to help yourself and hope that you can extend what you learn to other finance R packages.
This document discusses using hidden Markov models (HMM) for stock price prediction. HMMs can model time series data as a probabilistic finite state machine. The document explains that HMMs can handle new stock market data robustly and efficiently predict similar price patterns to past data. It provides an overview of HMM components like states, transition probabilities, and emission probabilities. The document also demonstrates building an HMM model on stock data using the RHMM package in R, including training the model with Baum-Welch and predicting state sequences with Viterbi.
This document proposes improvements to existing customer lifetime value models. It discusses deriving current models A and B, which discount average revenues over a subscriber's expected duration. The improvements consider estimating future cash flows and growth rates through regression analysis, accounting for other revenue streams, and incorporating the value of a subscriber's social network. The proposed model uses discounted cash flow analysis and least squares regression to forecast revenues and growth rates for each subscriber, considering revenues from mobile, TV, broadband and the revenues of subscribers within their social network. It requires subscriber revenue and call data to implement the analysis.
This document discusses building regression and classification models in R, including linear regression, generalized linear models, and decision trees. It provides examples of building each type of model using various R packages and datasets. Linear regression is used to predict CPI data. Generalized linear models and decision trees are built to predict body fat percentage. Decision trees are also built on the iris dataset to classify flower species.
This document discusses quantitative forecasting methods, including time series and causal models. It covers key time series components like trend, seasonality, and cycles. Three main time series methods are described: smoothing, trend projection, and trend projection adjusted for seasonal influence. Moving averages and exponential smoothing are explained as common techniques for forecasting stationary time series. The document also covers decomposing a time series into trend, seasonal, and irregular components. Regression methods are mentioned as another approach when a trend is present in the data.
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.
This talk builds on recent empirical work addressing the extent to which the transaction graph serves as an early-warning indicator for large financial losses. By identifying certain sub-graphs ('chainlets') with causal effect on price movements, we demonstrate the impact of extreme transaction graph activity on the intraday volatility of the Bitcoin prices series. In particular, we infer the loss distributions conditional on extreme chainlet activity. Armed with this empirical representation, we propose a modeling approach to explore conditions under which the market is stabilized by transaction graph aware agents.
CVA In Presence Of Wrong Way Risk and Early Exercise - Chiara Annicchiarico, ...Michele Beretta
We will show how to calibrate the main parameter of the model and how we have used it in order to evaluate the CVA and the CVAW of a one derivative portfolio with the possibility of early exercise.
IRJET - Candle Stick Chart for Stock Market PredictionIRJET Journal
This document discusses using candlestick charts for stock market prediction. It begins with an introduction to how computers can now process large amounts of stock data using data mining techniques. It then provides background on candlestick formations and some common patterns. The methodology section outlines the process of collecting historical stock data on open, high, low, and close prices to generate candlestick charts. These charts can be analyzed for patterns to predict future stock price movements. Related work discusses how candlestick patterns have been shown to outperform methods based only on price changes. The conclusion is that this candlestick chart approach may enable more accurate short-term stock price forecasts compared to other methods.
This paper analyzes the swap rates issued by the China Inter-bank Offered Rate(CHIBOR) and
selects the one-year FR007 daily data from January 1st, 2019 to June 30th, 2019 as a sample. To fit the data,
we conduct Monte Carlo simulation with several typical continuous short-term swap rate models such as the
Merton model, the Vasicek model, the CIR model, etc. These models contain both linear forms and nonlinear
forms and each has both drift terms and diffusion terms. After empirical analysis, we obtain the parameter
values in Euler-Maruyama scheme and relevant statistical characteristics of each model. The results show that
most of the short-term swap rate models can fit the swap rates and reflect the change of trend, while the CKLSO
model performs best.
This is a pretty broad exploration and tutorial of basic econometrics modeling techniques. It includes an introduction to quite a few multiple regression methods. It also includes an extensive coverage of model testing to ensure that your model is quantitatively sound and statistically robust using state of the art peer reviewing protocol.
Affine cascade models for term structure dynamics of sovereign yield curvesLAURAMICHAELA
Rafael Serrano profesor de la Universidad del Rosario
Resumen:
In the first part of the talk, I will present an introduction to stochastic affine short rate models for term structure of yield curves In the second part, I will focus on a recursive affine cascade with persistent factors for which the number of parameters, under specifications, is invariant to the size of the state space and converges to a stochastic limit as the number of factors goes to infinity. The cascade construction thereby overcomes dimensionality difficulties associated with general affine models. We contrast two specfifications of the model using linear Kalman filter for a panel of Colombian sovereign yields.
Solution manual for essentials of business analytics 1st editorvados ji
Full download link :
https://getbooksolutions.com/download/solution-manual-for-essentials-of-business-analytics-1st-edition/
Detail about Essentials of Business : (Click link bellow to view example )
https://getbooksolutions.com/wp-content/uploads/2016/11/Solution-Manual-for-Essentials-of-Business-Analytics-1st-editor.pdf
Table of Contents
Chapter 1. What Is Business Analytics?
Chapter 2. Descriptive Statistics.
Chapter 3. Data Visualization.
4. Linear Regression.
5. Time Series Analysis and Forecasting.
6. Data Mining.
7. Spreadsheet Models.
8. Linear Optimization Models.
9. Integer Linear Optimization.
10. Nonlinear Optimization Models.
11. Monte Carlo Simulation.
12. Decision Analysis.
Monte Carlo Simulations (UC Berkeley School of Information; July 11, 2019)Ivan Corneillet
My guest lecture on Monte Carlo simulations [or "how to be approximately right, now vs. precisely wrong, later (or never…)"] for the Managing Cyber Risk course of UC Berkeley School of Information's Cybersecurity Master.
Achieving Consistent Modeling Of VIX and Equities DerivativesVolatility
1) Discuss model complexity and calibration
2) Emphasize intuitive and robust calibration of sophisticated volatility models avoiding non-linear calibrations
3) Present local stochastic volatility models with jumps to achieve joint calibration to VIX options and (short-term) S&P500 options
4) Present two factor stochastic volatility model to fit both the short-term and long-term S&P500 option skews
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.
This document appears to be an assignment submission for a financial engineering course. It includes a plagiarism declaration signed by the student, Andrew Hair. The assignment contains 11 questions addressing interest rate derivatives and modeling using the Vasicek model. Code is provided in MATLAB to generate simulations and analyze interest rate data based on the questions.
1) The Monte Carlo method is used to determine the expected value of random variables by running multiple simulations or trials. 2) In this example, a Monte Carlo simulation is conducted in Microsoft Excel to calculate the expected total cost of a project with 6 activities that each have a range of possible costs. 3) The simulation involves generating random costs for each activity based on the minimum and maximum values, calculating a total cost, and repeating this process 362 times to estimate the expected project cost within 2% error.
1. The document describes three exercises related to statistical methods for financial institutions. The first exercise considers portfolio returns and risk, defines the expected return and variance of a portfolio, and discusses the difference between arithmetic and continuous returns. The second exercise analyzes stock price data to estimate parameters and risks, and simulates portfolio values with Monte Carlo methods. The third exercise covers factor models, the CAPM, and APT for analyzing portfolio performance.
2. Key steps include: computing the expected return and variance of a portfolio as a linear combination of stock returns and risks; estimating means, variances, and covariances from stock price data; simulating portfolio values over time; and decomposing portfolio risk using factor models. Confidence
This document discusses image compression using the discrete cosine transform (DCT). It develops simple Mathematica functions to compute the 1D and 2D DCT. The 1D DCT transforms a list of real numbers into elementary frequency components. It is computed via matrix multiplication or using the discrete Fourier transform with twiddle factors. The 2D DCT applies the 1D DCT to rows and then columns of an image, making it separable. These functions illustrate how Mathematica can be used to prototype image processing algorithms.
This document discusses image compression using the discrete cosine transform (DCT). It develops simple Mathematica functions to compute the 1D and 2D DCT. The 1D DCT transforms a list of real numbers into elementary frequency components. It is computed via matrix multiplication or using the discrete Fourier transform with twiddle factors. The 2D DCT applies the 1D DCT to rows and then columns, making it separable. These functions illustrate how Mathematica can be used to prototype image processing algorithms.
This document discusses machine learning techniques for actuarial science, including supervised learning methods like linear regression, generalized linear models (GLMs), generalized additive models (GAMs), elastic net, classification and regression trees (CART), random forests, boosted models, and stacked ensembles. It also briefly mentions deep learning techniques like multi-layer perceptrons, convolutional neural networks, and recurrent neural networks, as well as natural language processing applications like word2vec. Key advantages and disadvantages of each method are summarized.
This document discusses unsupervised learning techniques including principal component analysis (PCA), generalized low rank models (GLRM), K-means clustering, and deep learning autoencoders. PCA reduces dimensionality by identifying principal components that explain the most variance in the data. GLRM generalizes PCA to work with mixed data types. K-means clustering groups similar observations to identify homogeneous clusters. Autoencoders can detect anomalies through reconstructing input data. The document provides examples of applying these techniques to vehicle insurance data.
This document discusses machine learning concepts and applications in actuarial science. It introduces common machine learning algorithms like supervised learning algorithms for regression and classification, as well as unsupervised learning algorithms for clustering and dimensionality reduction. Examples of machine learning use cases in actuarial areas like pricing, claims reserving, and marketing are provided. The document also outlines best practices for machine learning projects including defining the business scope, data preparation, modeling, validation, and deployment. Specific algorithms like linear regression, decision trees, support vector machines, and K-nearest neighbors are explained. Tools for machine learning like H2O and interpretability techniques are also summarized.
Giorgio Alfredo Spedicato will give a presentation on machine learning and actuarial science. He will review machine learning theory, including unsupervised and supervised learning algorithms. He will provide examples using various datasets, including using unsupervised learning on an auto insurance dataset and supervised learning for credit scoring and claim severity prediction. Spedicato has experience as a data scientist and actuary and holds a PhD in Actuarial Science.
Meta Analysis Essentials provides an overview of meta-analysis techniques. Meta-analysis allows researchers to synthesize and aggregate results from different studies on the same topic to obtain more consistent statistics. It requires restructuring collected study materials. Meta-analyses typically compare one or two groups and estimate an effect size for each study. Estimates can be obtained using standard, random effects, or mixed effects models, with the latter two accounting for potential heterogeneity across studies. Conducting a meta-analysis requires input data on study details, measures, and results to estimate effect sizes and assess heterogeneity. Tools like R can be used to perform the analyses and generate outputs.
The markovchain R package provides tools for creating, representing, and analyzing discrete time Markov chains (DTMCs). It allows users to easily define DTMC objects, perform structural analysis of transition matrices, estimate transition matrices from data, and simulate stochastic sequences from DTMCs. The package aims to make working with Markov chains straightforward for R programmers through S4 classes and methods.
This document discusses traditional and alternative insurance options for catastrophe risks such as hurricanes, earthquakes, and floods. It provides details on:
- Traditional reinsurance and its limitations in fully meeting coverage demands, leading to the growth of alternative options like catastrophe (CAT) bonds.
- How CAT bonds work, including being issued by a special purpose vehicle to provide reinsurance coverage to primary insurers and allow access to capital markets.
- The components and uses of CAT models, which are computer simulations used to analyze catastrophe risk and loss exposures in property portfolios. CAT models help price coverage and allocate capital.
- Key considerations for primary insurers in deciding between traditional reinsurance or CAT bonds to transfer catastrophe
This document discusses important IT skills for actuaries to have. It recommends that actuaries have general skills in operating systems, Microsoft Office programs like Word and Excel, and have knowledge of databases and programming. Specifically, it suggests actuaries will write VBA code and know SQL. Statistical software mentioned includes SAS, R, and Python, with R gaining more acceptance. Professional actuarial software referenced includes programs from Willis Tower Watson for life and non-life insurance modeling and catastrophe modeling software. Examples given are using R for life and health insurance applications.
1. Actuaries are professionals who quantify and price financial risks for insurance companies. They determine premiums, reserves, and economic capital.
2. Becoming an actuary requires passing examinations in probability, mathematics, statistics, and finance. The requirements vary by country but it is a regulated profession everywhere.
3. Actuaries work on pricing and reserving for various insurance products including general insurance, life insurance, health insurance, and pensions. They also work in reinsurance, catastrophe modeling, and other non-traditional roles applying statistical skills.
This document discusses using machine learning techniques like logistic regression and random forests to build insurance retention models. It analyzes a dataset of 50,000 insurance policies to predict renewal probabilities and optimize renewal premiums. Logistic regression performs nearly as well as more complex methods like flexible discriminant analysis. The document also provides technical details on using R packages like caret and rms to fit and evaluate various predictive models for classification tasks.
- The document proposes using Generalized Additive Models for Location, Scale and Shape (GAMLSS) as an alternative methodology for claims reserving to provide both a point estimate and a measure of uncertainty.
- It describes how GAMLSS allows modeling of multiple distribution parameters, such as modeling the variance of incremental payments as a function of development year, to better fit the data.
- Numerical results on an example claims triangle show that GAMLSS provides a better fit than classical generalized linear models as measured by a lower GAIC, and results in a lower estimated variability for claims reserves.
This document discusses using R to price different types of insurance contracts. It provides examples of pricing life insurance, personal lines insurance, and excess of loss reinsurance contracts. For each type of insurance, it shows how to model costs and losses in R, calculate key metrics like expected claims and capital requirements, and determine final premiums. Code used in the examples is provided in an appendix.
This document discusses modeling underwriting premium risk for motor third party liability (MTPL) insurance under Italy's direct compensation (CARD) system. It provides an overview of the CARD system and the challenges it poses for pricing and risk modeling. Specifically, it notes that negative claim amounts are possible under CARD, the frequency and costs of both caused and suffered claims must be modeled, and historical experience is limited. It then describes the CARD forfeit structure and rules in more detail. The goal is to develop an internal model for assessing underwriting premium risk capital charges on an MTPL portfolio under the CARD system.
An actuarial model of drug prescriptions from a general practictioner is presented. The non life actuarial approach is applied to a health economics problem
3. Intro
The use of lifecontingencies R package (Spedicato 2013) to evaluate
annuities will be introduced.
lifecontingencies package provides a broad set of tools to perform actuarial
calculations on life insurances. It requires a recent version of R (>=3.0),
the markovchain package (Giorgio Alfredo Spedicato 2015) and Rcpp
(Eddelbuettel 2013).
This presentation is focused on actuarial evaluation of annuities present
value distribution from the perspective of a Pension Fund.
4. As a memo, the present value of a life annuity on a policyholder aged x is a
random variable that depends on the future lifetime, Kx , future cash flows
cj and future (real) discount factors vj =
1+rj
1+ij
− 1.
It can be written as ¨aKx +1
=
Kx
j=0
vj
∗ cj .
Therefore it is a function of three random variables: the residual life time,
Kt , the nominal (future) rates of interest, rt , and the (future) inflation rates
it , where t ∈ 0, 1
k
, . . . , Kt , .
5. We will calculate APV from a classical central baseline scenario (defined life
table and fixed financials hyphotheses). We will then allow for variability on
these hyphoteses.
In particular we will allow for process and parameter variance on the
demographical side of calculation. Stochastic interest rate and inflation
scenarios will be simulated as well.
Slides will contain key code snippets, figures and tables. The dedicated
repository (https://bitbucket.org/spedygiorgio/rininsurance2015)
collect the full code needed to replicate the results.
6. Collecting data
Collecting Financial from FRED
We will retrieve economics from Federal Reserve Economic Data using
quantmod package (Ryan 2015).
Demographic tables used to project life tables will come from Human
Mortality Database (University of California and Demographic Research
2015).
#retrieving Italian financial data from FRED
library(quantmod)
getSymbols(Symbols = 'ITACPIALLMINMEI',src='FRED') #CPI
getSymbols(Symbols='IRLTLT01ITM156N',
src='FRED') #Nominal IR (10Y Bond Yield)
7. we can observe a certain degree of structural dependency between i and r,
that suggests the use of cointegration analysis for modeling.
0%
5%
10%
15%
0%
5%
10%
15%
BondYield10YInflation
1990 1995 2000 2005 2010 2015
month
rate
Italian Inflation and Nominal Interest Rates since 1991
8. Collecting demographics from HMD
Retrieving data from Human Mortality Database (HMD) is easy as well
library(demography)
italyDemo<-hmd.mx("ITA", username="yourUN",
password="yourPW")
9. 0 20 40 60 80 100
−10−8−6−4−202
Italy: total death rates (1872−2009)
Age
Logdeathrate
10. Defining baseline actuarial hyphotheses
Our baseline hyphoteses are:
retiree age: x = 65, cohort 1950.
yearly pension benefit: 1, CPI indexed.
frequency of payment of 1
k
payments k = 12.
mortality model: Lee Carter.
no survivors benefit: no reversionary annuity component.
only one interest rate (r): 10 year governemnt bond yield.
Baseline inflation (i) and nominal interest rate (r) calculated as straight
average of 10 Years values between 1999 and 2014 (Euro Currency Era).
This yields a real discount factor around 2.4%.
11. xts package (Ryan and Ulrich 2014) functions have been used to calculate
baseline figures.
#use xts functions to calculate yearly averages
finHyph<-apply(apply.yearly(x =
italy.fin["1999/2014",2:1], FUN="mean"),2,"mean")
infl<-finHyph[1];nomRate<-finHyph[2]
realRate<-(1+nomRate)/(1+infl)-1
names(realRate)<-"RealRate"
c(nomRate, infl, realRate)
## BondYield10Y Inflation RealRate
## 0.04520074 0.02073512 0.02396862
12. Projecting mortality
Mortality dynamics will follow Lee Carter model (Lee and Carter 1992):
qx,t = eax +bx ∗kt +εx,t
,
We will start projecting a central scenario for mortality on which a baseline
life table can be derived for the 1950 cohort.
demography (Rob J Hyndman et al. 2011) and forecast (Hyndman and
Khandakar 2008) packages calibrate and perform Lee Carter’ model
projections respectively.
14. -The code below generates the matrix of prospective life tables
#getting and defining the life tables matrix
mortalityTable<-exp(italy.leecarter$ax+
italy.leecarter$bx%*%t(kt.full))
rownames(mortalityTable)<-seq(from=0, to=103)
colnames(mortalityTable)<-seq(from=1872,
to=1872+dim(mortalityTable)[2]-1)
15. The function below returns the yearly death probabilities for a given birth
cohort.
getCohortQx<-function(yearOfBirth)
{
colIndex<-which(colnames(mortalityTable)
==yearOfBirth) #identify
#the column corresponding to the cohort
#definex the probabilities from which
#the projection is to be taken
maxLength<-min(nrow(mortalityTable)-1,
ncol(mortalityTable)-colIndex)
qxOut<-numeric(maxLength+1)
for(i in 0:maxLength)
qxOut[i+1]<-mortalityTable[i+1,colIndex+i]
#fix: we add a fictional omega age where
#death probability = 1
qxOut<-c(qxOut,1)
return(qxOut)
}
16. Now we can get a baseline projected life table for a 1950 born.
#generate the life tables
qx1950<-getCohortQx(yearOfBirth = 1950)
lt1950<-probs2lifetable(probs=qx1950,type="qx",
name="Baseline")
at1950Baseline<-new("actuarialtable",x=lt1950@x,
lx=lt1950@lx,interest=realRate)
17. 0 20 40 60 80 100
0200040006000800010000
life table Generic life table
x values
populationatrisk
18. Variability assessment
Process variance
It is now easy to assess the expected curtate lifetime, ˚e65 and the APV of
the annuity ¨a12
65, for x = 65.
#curtate lifetime @x=65
ex65.base<-exn(object = at1950Baseline,x = 65)
names(ex65.base)<-"ex65"
#APV of an annuity, allowing for fractional payment
ax65.base<-axn(actuarialtable = at1950Baseline,
x=65,k = 12);names(ax65.base)<-"ax65"
c(ex65.base,ax65.base)
## ex65 ax65
## 18.72669 14.95836
19. It is possible to simulate the process variance (due to “pure” chance on
residual life time) of both Kt and ¨aKx +1
=
Kx
j=0
vj
∗ cj .
#simulate curtate lifetime
lifesim<-rLife(n=1e4,object=at1950Baseline,x=65,k=12,type = "Kx")
c(mean(lifesim),sd(lifesim))
## [1] 19.057092 8.263257
#simulate annuity present value
annuitysim<-rLifeContingencies(n=1e4,lifecontingency="axn",
object=at1950Baseline,x=65,k=12,parallel=TRUE)
c(mean(annuitysim),sd(annuitysim))
## [1] 14.943719 5.548229
20. 0.00
0.01
0.02
0.03
0.04
0.05
0 10 20 30 40
Kt
density Remaining lifetime
0.00
0.02
0.04
0.06
0.08
0 10 20
APV
density
Annuity Actuarial Present Value simulation
Process Variance simulation
21. Stochastic life tables
Estimation variance due to the demographic component arises from
uncertainty in demographic assumption (stochastic life tables).
We take into account this source of variability generating random life tables
by randomizing kt projections and by sampling from εx,t on the Lee Carter
above mentioned formula.
22. The code that follows integrates the simulation of parameter and process
variance on the demographic component.
###nesting process variance and parameter variance
numsim.parvar=31
numsim.procvar=31
### simulating parameter variance
tablesList<-list()
for(i in 1:numsim.parvar) tablesList[[i]] <-
tableSimulator(lcObj = italy.leecarter,
kt.model = italy.kt.model,
coort = 1950,
type = 'simulated',
ltName = paste("table",i),
rate=realRate
)
### simulating process variance
lifesim.full<-as.numeric(sapply(X=tablesList, FUN="rLife",n=numsim.procv
annuitysim.full<-as.numeric(sapply(X=tablesList, FUN="rLifeContingencies
23. Varying financial assumptions
Changing nominal interest rate assumption
We assume only one financial asset: 10 years Gvt Bond.
Interest rate dynamic follows a Vasicek model,
drt = λ ∗ (rt − µ) ∗ dt + σ ∗ dWt .
Therefore parameters can be estimated by least squares from the equation
St = a ∗ St−1 + b + εt , as shown below. We have used the approach shown
in http://www.sitmo.com/article/
calibrating-the-ornstein-uhlenbeck-model/.
λ = −
lna
δ
µ =
b
1 − a
σ = sd(ε) −
2 ∗ ln (a)
δ ∗ (1 − a2)
24. The function that follows calibrates the Vasicek interest rate mode on
Italian data since 1991.
calibrateVasicek<-function(x, delta=1) {
y<-as.zoo(x)
x<-lag(y,-1,na.pad=TRUE)
myDf<-data.frame(y=y,x=x)
linMod <- lm(y~x,data=myDf)
a<-coef(linMod)[2]
b<-coef(linMod)[1]
lambda<- as.numeric(-log(a)/delta)
mu <- as.numeric(b/(1-a))
sigma <- as.numeric(((-2*log(a))/(delta*(1-a^2)))^.5*sd(linMod$residu
out<-list(lamdba=lambda, mu=mu, sigma=sigma)
return(out)
}
25. The calibrated parameters follows. However the long term average has been
judgmentally fixed to 4.52%.
They will be used to simulate Vasicek - driven interest rates paths.
#calibrate
italianRatesVasicek<-calibrateVasicek(x =as.numeric(italy.fin[,1]),
delta=1/12)
italianRatesVasicek
## $lamdba
## [1] 0.1129055
##
## $mu
## [1] 0.01704393
##
## $sigma
## [1] 0.0102649
#simulate
randomInterestRateWalk<-ts(VasicekSimulations(M = 1,N = 40*12,r0 = 0.04,
italianRatesVasicek$sigma ,dt = 1/12)[,1],start=c(2015,4),frequency=12)
26. One Vasicek interest rate walk
month
nominalinterestrate
2020 2030 2040 2050
0.000.020.040.060.080.10
27. Modeling inflation dynamic
The dependency between nominal rates and inflation is well know.
Cointegration analysis is needed to avoid spurious regression.
We have assumed the their relationship to be linear inft = α + β ∗ rt + γt .
Cointegration analysis on annualized data was peformed using package vars
(Pfaff 2008). One cointegrating relationship was found to be quite well
supported by empirical data.
29. Pulling all together
This algorithm simulatrs the distribution of annuity’s:
1. simulate Kt .
2. Project the fixed cash flow vector 1
k
for all t in 0, 1
k
, 2
k
, . . . , Kt .
3. Simulate a rt path.
4. Simulate a it path by the relation it = α + β ∗ rt + γt .
5. Determine real interest rate vector and discount.
30. The figure below shows the distribution of the Kt and
¨aK+1
=
Kx
j=0
vj
∗ cj after allowing for process and parameter variance
(for the demographic component).
0.00
0.02
0.04
0 10 20 30
Kt
density
Residual Curtate Life Time Distribution
0.00
0.02
0.04
0.06
0 10 20 30 40
Present Value
density
Annuity Present Value Simulated Distribution
Full Stochastic simulation
31. Expected value changes moderately and standard deviations increases
slightly for Kx and ¨aKx +1
=
Kx
j=0
vj
∗ cj distributions.
#central scenario remark
c(ex65.base,ax65.base)
## ex65 ax65
## 18.72669 14.95836
#assessing impact on expected value
apply(final.simulation,2,mean)/apply(processVarianceSimulations,2,mean)
## residualLifetime annuityAPV
## 0.9836045 1.0722882
#assessing impact on volatility
apply(final.simulation,2,sd)/apply(processVarianceSimulations,2,sd)
## residualLifetime annuityAPV
## 1.173815 1.125270
32. Other package’s features
Even if not discussed in the presentation, it is worth to remark that
lifecontingencies package allows to calculate also the impact of reversionary
annuity benefits (see below the calculation for axy . Multiple decrements will
be fully supported within 2015.
#baseline benefit
ax65.base
## ax65
## 14.95836
#allowign for reversionary on 62
axn(actuarialtable = at1950Baseline,x = 65,k=12)+
(axn(actuarialtable = at1950Baseline,x = 62,k=12)-
axyzn(tablesList = list(at1950Baseline,at1950Baseline),
x = c(65,62),status = "joint",k = 12))
## [1] 18.85357
33. Bibliography I
Eddelbuettel, Dirk. 2013. Seamless R and C++ Integration with Rcpp. New
York: Springer.
Giorgio Alfredo Spedicato. 2015. Markovchain: Discrete Time Markov Chains
Made Easy.
Hyndman, Rob J, and Yeasmin Khandakar. 2008. “Automatic Time Series
Forecasting: The Forecast Package for R.” Journal of Statistical Software 26 (3):
1–22. http://ideas.repec.org/a/jss/jstsof/27i03.html.
Lee, Ronald D, and Lawrence R Carter. 1992. “Modeling and Forecasting US
Mortality.” Journal of the American Statistical Association 87 (419). Taylor &
Francis Group: 659–71.
Pfaff, Bernhard. 2008. “VAR, SVAR and SVEC Models: Implementation Within
R Package vars.” Journal of Statistical Software 27 (4).
http://www.jstatsoft.org/v27/i04/.
Rob J Hyndman, Heather Booth, Leonie Tickle, and John Maindonald. 2011.
Demography: Forecasting Mortality, Fertility, Migration and Population Data.
http://CRAN.R-project.org/package=demography.
Ryan, Jeffrey A. 2015. Quantmod: Quantitative Financial Modelling Framework.
http://CRAN.R-project.org/package=quantmod.
34. Bibliography II
Ryan, Jeffrey A., and Joshua M. Ulrich. 2014. Xts: EXtensible Time Series.
http://CRAN.R-project.org/package=xts.
Spedicato, Giorgio Alfredo. 2013. “The lifecontingencies Package: Performing
Financial and Actuarial Mathematics Calculations in R.” Journal of Statistical
Software 55 (10): 1–36. http://www.jstatsoft.org/v55/i10/.
University of California, and Max Planck Institute for Demographic Research.
2015. “Human Mortality DataBase.” Available at www.mortality.org or
www.humanmortality.de (data downloaded on 14th June 2015).