This document provides an overview of the course ECO568 - Uncertainty and Financial Markets. It discusses key concepts in financial economics including rationality, arbitrage, and the law of one price. It also outlines the course, which will cover topics like no-arbitrage pricing, investment theory, and term structure models. The goal is to develop a consistent theory to explain stylized facts about financial markets like efficiency, risk premiums, and asset return correlations.
The document provides an introduction to quantitative finance concepts including option pricing models. It begins with an outline and terminology. It then covers the Black-Scholes option pricing model, which uses stochastic calculus to derive a partial differential equation for pricing European options. The document also discusses replicating strategies in discrete and continuous time models, as well as extensions like American options and the Greeks.
The Capital Asset Pricing Model (CAPM) asserts that the expected return of an asset is determined by its sensitivity to non-diversifiable market risk, as measured by beta. Under CAPM, the expected return of an asset is equal to the risk-free rate plus a risk premium that is proportional to the asset's beta. CAPM provides a model for pricing assets and estimating the expected return of risky projects based on an asset's systematic risk.
This document discusses real option valuation techniques for technology projects. It begins by providing examples of real options like options to abandon or expand a project. It then covers various valuation models like decision trees, binomial models, and Monte Carlo simulations. These models can value flexibility and account for uncertainty. The document concludes by discussing Captum Capital which provides valuation and consulting services, including upcoming events on their valuation masterclass and workshop on technology evaluation.
The document discusses the arbitrage pricing theory (APT), which relates a security's expected return to multiple common risk factors. It provides examples of how the APT can be used to model returns based on factors like inflation, GDP growth, and exchange rates. The APT assumes perfect capital markets, homogeneous investor expectations, and allows short selling and arbitrage opportunities. It implies a linear relationship between expected returns and factor sensitivities similar to the capital asset pricing model. Empirical tests provide some support for the APT but also have limitations.
The document discusses the Arbitrage Pricing Theory (APT), which is an equilibrium factor model of security returns. APT assumes capital markets are perfectly competitive, investors prefer more wealth, and the price-generating process follows a multi-factor model. APT states that no arbitrage opportunities exist if expected returns are a linear function of various macroeconomic factors. Attempts to arbitrage will force a linear relationship between risk and return.
This document discusses various asset pricing models, including the Capital Asset Pricing Model (CAPM) and the Security Market Line (SML). It provides an overview of the key assumptions and components of the CAPM, such as the capital market line, market portfolio, beta, and the security market line equation. An example is shown of calculating expected returns based on the SML. The differences between the capital market line and security market line are also explained.
The Arbitrage Pricing Theory (APT) provides an alternative to the Capital Asset Pricing Model (CAPM) for estimating expected returns. The APT assumes returns are generated by multiple systematic risk factors rather than a single market factor. It allows for assets to be mispriced and does not require assumptions of a market portfolio or homogeneous expectations. Under the APT, the expected return of an asset is equal to the risk-free rate plus the product of each risk factor's premium and the asset's sensitivity to that factor.
1) Arbitrage Pricing Theory (APT) is an equilibrium factor model that states a security's expected return is determined by its sensitivity to various macroeconomic factors.
2) APT assumes capital markets are perfectly competitive and investors prefer more wealth to less. The price-generating process can be modeled as a multi-factor model.
3) According to APT, if the risk-return relationship is non-linear, arbitrage opportunities exist as risk-free portfolios can be constructed with positive expected returns. Attempts to arbitrage will force the relationship between risk and return to become linear.
The document provides an introduction to quantitative finance concepts including option pricing models. It begins with an outline and terminology. It then covers the Black-Scholes option pricing model, which uses stochastic calculus to derive a partial differential equation for pricing European options. The document also discusses replicating strategies in discrete and continuous time models, as well as extensions like American options and the Greeks.
The Capital Asset Pricing Model (CAPM) asserts that the expected return of an asset is determined by its sensitivity to non-diversifiable market risk, as measured by beta. Under CAPM, the expected return of an asset is equal to the risk-free rate plus a risk premium that is proportional to the asset's beta. CAPM provides a model for pricing assets and estimating the expected return of risky projects based on an asset's systematic risk.
This document discusses real option valuation techniques for technology projects. It begins by providing examples of real options like options to abandon or expand a project. It then covers various valuation models like decision trees, binomial models, and Monte Carlo simulations. These models can value flexibility and account for uncertainty. The document concludes by discussing Captum Capital which provides valuation and consulting services, including upcoming events on their valuation masterclass and workshop on technology evaluation.
The document discusses the arbitrage pricing theory (APT), which relates a security's expected return to multiple common risk factors. It provides examples of how the APT can be used to model returns based on factors like inflation, GDP growth, and exchange rates. The APT assumes perfect capital markets, homogeneous investor expectations, and allows short selling and arbitrage opportunities. It implies a linear relationship between expected returns and factor sensitivities similar to the capital asset pricing model. Empirical tests provide some support for the APT but also have limitations.
The document discusses the Arbitrage Pricing Theory (APT), which is an equilibrium factor model of security returns. APT assumes capital markets are perfectly competitive, investors prefer more wealth, and the price-generating process follows a multi-factor model. APT states that no arbitrage opportunities exist if expected returns are a linear function of various macroeconomic factors. Attempts to arbitrage will force a linear relationship between risk and return.
This document discusses various asset pricing models, including the Capital Asset Pricing Model (CAPM) and the Security Market Line (SML). It provides an overview of the key assumptions and components of the CAPM, such as the capital market line, market portfolio, beta, and the security market line equation. An example is shown of calculating expected returns based on the SML. The differences between the capital market line and security market line are also explained.
The Arbitrage Pricing Theory (APT) provides an alternative to the Capital Asset Pricing Model (CAPM) for estimating expected returns. The APT assumes returns are generated by multiple systematic risk factors rather than a single market factor. It allows for assets to be mispriced and does not require assumptions of a market portfolio or homogeneous expectations. Under the APT, the expected return of an asset is equal to the risk-free rate plus the product of each risk factor's premium and the asset's sensitivity to that factor.
1) Arbitrage Pricing Theory (APT) is an equilibrium factor model that states a security's expected return is determined by its sensitivity to various macroeconomic factors.
2) APT assumes capital markets are perfectly competitive and investors prefer more wealth to less. The price-generating process can be modeled as a multi-factor model.
3) According to APT, if the risk-return relationship is non-linear, arbitrage opportunities exist as risk-free portfolios can be constructed with positive expected returns. Attempts to arbitrage will force the relationship between risk and return to become linear.
This document provides an overview of the course "ECO568 - Uncertainty and Financial Markets". It discusses three key concepts:
1) No-arbitrage and the law of one price, which states that identical assets must have the same price.
2) State-price vectors, which provide a way to price assets consistently using an equivalent risk-neutral probability measure.
3) Complete markets, where the number of traded assets equals the number of states of the world, allowing any payoff to be replicated.
Real time information reconstruction -The Prediction Marketraghavr186
This document summarizes an approach to analyzing prediction markets using convex optimization. It discusses both offline and online formulations of the problem. The offline formulation involves accepting bids to maximize profit, which can be modeled as a linear program. Uniqueness of the solution is analyzed. The online formulation updates the model sequentially as bids arrive in real time. Various choices for the objective function are discussed, balancing risk aversion with expected gain. Truthfulness of bids is also addressed.
Discrete math is the branch of mathematics that does not rely on limits. It is well-suited to describe computer science concepts precisely as computers operate discretely in discrete steps. The document provides an overview of topics in discrete math including logic, sets, proofs, counting, and graph theory. These topics provide the tools needed for creating and analyzing sophisticated algorithms.
This document discusses methods for computing upper and lower bounds on the cumulative distribution function (CDF) of products of random variables. It presents Chebyshev inequalities that provide bounds on the probability that the product is less than or equal to a given value γ. For the upper bound Upγ), it shows that this can be computed by formulating an optimization problem and solving a finite semidefinite program that leverages duality. The lower bound Lpγ) can similarly be computed through optimization. These bounds provide useful information about the CDF without fully specifying the distribution.
This document discusses discrete structures and logical operators. It defines logical connectives like negation, conjunction, disjunction, exclusive or, implication, and biconditional. It provides examples of using these connectives to write compound propositions and their truth tables. It also covers translating between English statements and logical expressions. Additional topics include tautologies, contradictions, logical equivalence, De Morgan's laws, and other laws of logic. Worked examples are provided to demonstrate simplifying and proving equivalence of logical propositions.
Artificial intelligence knowledge representation and learningannmariyajaimon2023
The document discusses knowledge representation and logical agents. It introduces knowledge-based agents and how they use a knowledge base to represent knowledge and reason about it. The document then discusses propositional logic and how it can be used to represent the Wumpus world environment. It provides examples of logical inference using propositional rules derived from the Wumpus world.
This chapter introduces a simple representative agent macroeconomic model with a single consumer and firm. The consumer maximizes utility from consumption and leisure subject to a budget constraint. The firm maximizes profits by choosing optimal capital and labor inputs. A competitive equilibrium exists where markets clear, consumers optimize, and firms optimize given prices. The competitive equilibrium is also a Pareto optimum, so the model implies no role for government intervention. An example is provided using Cobb-Douglas production and constant relative risk aversion utility functions to illustrate the model.
This document discusses risk and return in finance. It defines risk as variability in returns and explains how to measure risk statistically using measures like variance and standard deviation. It also discusses different types of risk like diversifiable and non-diversifiable risk. The document then introduces the Capital Asset Pricing Model (CAPM), which uses an asset's beta to determine its required return based on the security market line. The CAPM model provides a way to quantify risk premiums and determine adequate returns for assets based on their non-diversifiable risk.
Fair valuation of participating life insurance contracts with jump riskAlex Kouam
A C++ based program which prices the fair value of a participating life insurance whereby the underlying follows a Kou process and the insurer's default occurs only at contract's maturity.
This document provides an introduction to propositional logic and logical connectives. Some key points:
- Propositional logic deals with propositions that can be either true or false. Common logical connectives are negation, conjunction, disjunction, implication, biconditional.
- Truth tables are used to define the semantics and truth values of logical connectives and compound propositions.
- Logical equivalences allow replacing a proposition with an equivalent proposition to simplify expressions or arguments. Equivalences can be shown using truth tables or known equivalence rules.
- Propositional logic and logical reasoning form the basis of mathematical reasoning and are useful in areas like computer science, programming, and satisfiability problems.
Agent-based economic modeling often requires the determination of an initial equilibrium price vector. Calculating this directly requires algorithms of exponential computational complexity. It is known that a partial equilibrium price can be estimated using a median of trades. This paper explores the possibility of a multivariate generalization of this technique using depth functions.
The document provides an overview of knowledge representation and logic. It discusses knowledge-based agents and how they use a knowledge base to represent facts about the world through sentences expressed in a knowledge representation language. It then covers different knowledge representation schemas including propositional logic, first-order logic, rules, networks, and structures. The document also discusses inference, different types of logic, and knowledge representation languages.
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# Underachievers can find peer developed notes that break down lecture and study material in a way that they can understand
# Students can earn better grades, save time and study effectively
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State Space c-Reductions of Concurrent Systems in Rewriting Logic @ ETAPS Wor...Alberto Lluch Lafuente
We present c-reductions, a state space reduction technique. The rough idea is to exploit some equivalence relation on states (possibly capturing system regularities) that preserves behavioral properties, and explore the induced quotient system. This is done by means of a canonizer function, which maps each state into one (of the) canonical representative(s) of its equivalence class. The approach exploits the expressiveness of rewriting logic and its realization in Maude to enjoy several advantages over similar approaches: flexibility and simplicity in the definition of the reductions (supporting not only traditional symmetry reductions, but also name reuse and name abstraction); reasoning support for checking and proving correctness of the reductions; and automatization of the reduction infrastructure via Maude's meta-programming features. The approach has been validated over a set of representative case studies, exhibiting comparable results with respect to other tools.
This chapter discusses basic concepts of option management including European and American call and put options. It covers pricing options, arbitrage opportunities, valuing forward contracts, and put-call parity. Several exercises are provided to practice these concepts, such as calculating option prices in a one-period binomial model, identifying arbitrage opportunities between stock and option prices, and determining upper and lower bounds for option prices.
Discrete space time option pricing forum fsrIlya Gikhman
This document presents a formal approach to pricing derivatives in discrete space-time. The primary principle introduced is the notion of equality of investments, which is based on investors aiming to achieve a greater return. Two investments are considered equal if their instantaneous rates of return are equal at any given moment in time. The approach also uses the concept of cash flows and a series of transactions to define investments more broadly. An example is provided to illustrate pricing methodology, where the price of a call option written on a stock is a random variable that takes on different values depending on the stock price scenario.
This document discusses how family history can impact life insurance premiums. It reviews existing literature on relationships between family members' lifespans, such as husbands and wives or parents and children. Genealogical data is used to analyze dependencies between generations, like grandchildren and grandparents. Quantities important for life insurance are calculated based on family information, showing how premiums may differ depending on how many family members are still alive. The goal is to better understand how family history can influence longevity and mortality risk factors used in life insurance underwriting.
Family History and Life Insurance (UConn actuarial seminar)Arthur Charpentier
This document discusses how family history can impact life insurance premiums. It reviews existing literature on relationships between family members' lifespans. The document analyzes a genealogical dataset to study dependencies between husbands and wives, parents and children, and grandparents and grandchildren. It finds modest but robust correlations between related individuals' lifespans. This dependency is quantified for various life insurance metrics like annuities and whole life insurance, showing family history can impact premiums.
Talk at the modcov19 CNRS workshop, en France, to present our article COVID-19 pandemic control: balancing detection policy and lockdown intervention under ICU sustainability
This document provides an overview of the course "ECO568 - Uncertainty and Financial Markets". It discusses three key concepts:
1) No-arbitrage and the law of one price, which states that identical assets must have the same price.
2) State-price vectors, which provide a way to price assets consistently using an equivalent risk-neutral probability measure.
3) Complete markets, where the number of traded assets equals the number of states of the world, allowing any payoff to be replicated.
Real time information reconstruction -The Prediction Marketraghavr186
This document summarizes an approach to analyzing prediction markets using convex optimization. It discusses both offline and online formulations of the problem. The offline formulation involves accepting bids to maximize profit, which can be modeled as a linear program. Uniqueness of the solution is analyzed. The online formulation updates the model sequentially as bids arrive in real time. Various choices for the objective function are discussed, balancing risk aversion with expected gain. Truthfulness of bids is also addressed.
Discrete math is the branch of mathematics that does not rely on limits. It is well-suited to describe computer science concepts precisely as computers operate discretely in discrete steps. The document provides an overview of topics in discrete math including logic, sets, proofs, counting, and graph theory. These topics provide the tools needed for creating and analyzing sophisticated algorithms.
This document discusses methods for computing upper and lower bounds on the cumulative distribution function (CDF) of products of random variables. It presents Chebyshev inequalities that provide bounds on the probability that the product is less than or equal to a given value γ. For the upper bound Upγ), it shows that this can be computed by formulating an optimization problem and solving a finite semidefinite program that leverages duality. The lower bound Lpγ) can similarly be computed through optimization. These bounds provide useful information about the CDF without fully specifying the distribution.
This document discusses discrete structures and logical operators. It defines logical connectives like negation, conjunction, disjunction, exclusive or, implication, and biconditional. It provides examples of using these connectives to write compound propositions and their truth tables. It also covers translating between English statements and logical expressions. Additional topics include tautologies, contradictions, logical equivalence, De Morgan's laws, and other laws of logic. Worked examples are provided to demonstrate simplifying and proving equivalence of logical propositions.
Artificial intelligence knowledge representation and learningannmariyajaimon2023
The document discusses knowledge representation and logical agents. It introduces knowledge-based agents and how they use a knowledge base to represent knowledge and reason about it. The document then discusses propositional logic and how it can be used to represent the Wumpus world environment. It provides examples of logical inference using propositional rules derived from the Wumpus world.
This chapter introduces a simple representative agent macroeconomic model with a single consumer and firm. The consumer maximizes utility from consumption and leisure subject to a budget constraint. The firm maximizes profits by choosing optimal capital and labor inputs. A competitive equilibrium exists where markets clear, consumers optimize, and firms optimize given prices. The competitive equilibrium is also a Pareto optimum, so the model implies no role for government intervention. An example is provided using Cobb-Douglas production and constant relative risk aversion utility functions to illustrate the model.
This document discusses risk and return in finance. It defines risk as variability in returns and explains how to measure risk statistically using measures like variance and standard deviation. It also discusses different types of risk like diversifiable and non-diversifiable risk. The document then introduces the Capital Asset Pricing Model (CAPM), which uses an asset's beta to determine its required return based on the security market line. The CAPM model provides a way to quantify risk premiums and determine adequate returns for assets based on their non-diversifiable risk.
Fair valuation of participating life insurance contracts with jump riskAlex Kouam
A C++ based program which prices the fair value of a participating life insurance whereby the underlying follows a Kou process and the insurer's default occurs only at contract's maturity.
This document provides an introduction to propositional logic and logical connectives. Some key points:
- Propositional logic deals with propositions that can be either true or false. Common logical connectives are negation, conjunction, disjunction, implication, biconditional.
- Truth tables are used to define the semantics and truth values of logical connectives and compound propositions.
- Logical equivalences allow replacing a proposition with an equivalent proposition to simplify expressions or arguments. Equivalences can be shown using truth tables or known equivalence rules.
- Propositional logic and logical reasoning form the basis of mathematical reasoning and are useful in areas like computer science, programming, and satisfiability problems.
Agent-based economic modeling often requires the determination of an initial equilibrium price vector. Calculating this directly requires algorithms of exponential computational complexity. It is known that a partial equilibrium price can be estimated using a median of trades. This paper explores the possibility of a multivariate generalization of this technique using depth functions.
The document provides an overview of knowledge representation and logic. It discusses knowledge-based agents and how they use a knowledge base to represent facts about the world through sentences expressed in a knowledge representation language. It then covers different knowledge representation schemas including propositional logic, first-order logic, rules, networks, and structures. The document also discusses inference, different types of logic, and knowledge representation languages.
FellowBuddy.com is an innovative platform that brings students together to share notes, exam papers, study guides, project reports and presentation for upcoming exams.
We connect Students who have an understanding of course material with Students who need help.
Benefits:-
# Students can catch up on notes they missed because of an absence.
# Underachievers can find peer developed notes that break down lecture and study material in a way that they can understand
# Students can earn better grades, save time and study effectively
Our Vision & Mission – Simplifying Students Life
Our Belief – “The great breakthrough in your life comes when you realize it, that you can learn anything you need to learn; to accomplish any goal that you have set for yourself. This means there are no limits on what you can be, have or do.”
Like Us - https://www.facebook.com/FellowBuddycom
State Space c-Reductions of Concurrent Systems in Rewriting Logic @ ETAPS Wor...Alberto Lluch Lafuente
We present c-reductions, a state space reduction technique. The rough idea is to exploit some equivalence relation on states (possibly capturing system regularities) that preserves behavioral properties, and explore the induced quotient system. This is done by means of a canonizer function, which maps each state into one (of the) canonical representative(s) of its equivalence class. The approach exploits the expressiveness of rewriting logic and its realization in Maude to enjoy several advantages over similar approaches: flexibility and simplicity in the definition of the reductions (supporting not only traditional symmetry reductions, but also name reuse and name abstraction); reasoning support for checking and proving correctness of the reductions; and automatization of the reduction infrastructure via Maude's meta-programming features. The approach has been validated over a set of representative case studies, exhibiting comparable results with respect to other tools.
This chapter discusses basic concepts of option management including European and American call and put options. It covers pricing options, arbitrage opportunities, valuing forward contracts, and put-call parity. Several exercises are provided to practice these concepts, such as calculating option prices in a one-period binomial model, identifying arbitrage opportunities between stock and option prices, and determining upper and lower bounds for option prices.
Discrete space time option pricing forum fsrIlya Gikhman
This document presents a formal approach to pricing derivatives in discrete space-time. The primary principle introduced is the notion of equality of investments, which is based on investors aiming to achieve a greater return. Two investments are considered equal if their instantaneous rates of return are equal at any given moment in time. The approach also uses the concept of cash flows and a series of transactions to define investments more broadly. An example is provided to illustrate pricing methodology, where the price of a call option written on a stock is a random variable that takes on different values depending on the stock price scenario.
This document discusses how family history can impact life insurance premiums. It reviews existing literature on relationships between family members' lifespans, such as husbands and wives or parents and children. Genealogical data is used to analyze dependencies between generations, like grandchildren and grandparents. Quantities important for life insurance are calculated based on family information, showing how premiums may differ depending on how many family members are still alive. The goal is to better understand how family history can influence longevity and mortality risk factors used in life insurance underwriting.
Family History and Life Insurance (UConn actuarial seminar)Arthur Charpentier
This document discusses how family history can impact life insurance premiums. It reviews existing literature on relationships between family members' lifespans. The document analyzes a genealogical dataset to study dependencies between husbands and wives, parents and children, and grandparents and grandchildren. It finds modest but robust correlations between related individuals' lifespans. This dependency is quantified for various life insurance metrics like annuities and whole life insurance, showing family history can impact premiums.
Talk at the modcov19 CNRS workshop, en France, to present our article COVID-19 pandemic control: balancing detection policy and lockdown intervention under ICU sustainability
The document discusses research on the relationship between family history and life insurance. It summarizes existing literature showing modest but robust connections between the lifespans of family members like spouses, parents and children, and grandparents and grandchildren. The document then presents analyses using a genealogical dataset, finding correlations between related individuals' lifespans. It explores how these family dependencies could impact life insurance premiums and quantities like annuities, widow's pensions, and life expectancies.
This document discusses the use of machine learning techniques in actuarial science and insurance. It begins with an overview of predictive modeling applications in insurance such as fraud detection, premium computation, and claims reserving. It then covers traditional econometric techniques like Poisson and gamma regression models and how machine learning is emerging as an alternative. The document emphasizes evaluating model goodness of fit and uncertainty, and addresses issues like price discrimination and fairness.
This document summarizes a paper on reinforcement learning in economics and finance. It introduces reinforcement learning concepts like agents, environments, actions, rewards, and states. It then discusses applications of reinforcement learning frameworks in economic problems like inventory management, consumption and income dynamics, and experiments. Finally, it notes connections between reinforcement learning and other fields like operations research, stochastic games, and finance.
This document models the COVID-19 pandemic using a compartmental SIDUHR+/- model that divides the population into susceptible (S), infected asymptomatic (I-), infected symptomatic (I+), recovered asymptomatic (R-), recovered symptomatic (R+), hospitalized (H), ICU (U), and dead (D) categories. Optimal lockdown policies are determined by minimizing costs related to deaths, economic impact, testing needs, and immunity while ensuring ICU sustainability. Increasing ICU capacity allows less stringent lockdown policies while achieving similar outcomes. Faster detection of asymptomatic cases through increased testing also enables more flexible lockdown policies.
The document summarizes research on using genealogical data to model dependencies in life spans between family members and quantify the impact on insurance premiums. It presents analysis of husband-wife, parent-child, and grandparent-grandchild relationships, showing dependencies exist. Mortality rates, life expectancies, and insurance quantities like annuities are estimated conditionally based on family history information.
The document discusses natural language processing techniques including word embeddings, text classification using naive Bayes classifiers, and probabilistic language models. It provides examples of part-of-speech tagging and analyzing sentiment. Key concepts covered include the bag-of-words assumption, n-gram models, and maximum likelihood estimation. Various papers on related topics are cited throughout.
This document discusses network representation and analysis. It defines networks as consisting of nodes (vertices) and edges, and describes different ways to represent networks mathematically using adjacency matrices, incidence matrices, and Laplacian matrices. It also discusses visualizing networks using multidimensional scaling and plotting them in R. Special types of networks like complete graphs and random graphs are briefly introduced.
The document discusses various techniques for classifying pictures using neural networks, including convolutional neural networks. It describes how convolutional neural networks can be used to classify images by breaking them into overlapping tiles, applying small neural networks to each tile, and pooling the results. The document also discusses using recurrent neural networks to classify videos by treating them as higher-dimensional tensors.
The document discusses using unusual data sources in insurance. It provides examples of using pictures, text, social media data, telematics, and satellite imagery in insurance. It also discusses challenges in analyzing complex and high-dimensional data from these sources and introduces machine learning tools like PCA, generalized linear models, and evaluating models using loss, risk, and cross-validation.
This document discusses classification and goodness of fit in machine learning. It introduces concepts like confusion matrices, ROC curves, and measures like sensitivity, specificity, and AUC. ROC curves are constructed by plotting the true positive rate vs. false positive rate for different classification thresholds. The AUC can measure classifier performance, with higher values indicating better classification. Chi-square tests and bootstrapping are also discussed for evaluating goodness of fit.
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This PowerPoint compilation offers a comprehensive overview of 20 leading innovation management frameworks and methodologies, selected for their broad applicability across various industries and organizational contexts. These frameworks are valuable resources for a wide range of users, including business professionals, educators, and consultants.
Each framework is presented with visually engaging diagrams and templates, ensuring the content is both informative and appealing. While this compilation is thorough, please note that the slides are intended as supplementary resources and may not be sufficient for standalone instructional purposes.
This compilation is ideal for anyone looking to enhance their understanding of innovation management and drive meaningful change within their organization. Whether you aim to improve product development processes, enhance customer experiences, or drive digital transformation, these frameworks offer valuable insights and tools to help you achieve your goals.
INCLUDED FRAMEWORKS/MODELS:
1. Stanford’s Design Thinking
2. IDEO’s Human-Centered Design
3. Strategyzer’s Business Model Innovation
4. Lean Startup Methodology
5. Agile Innovation Framework
6. Doblin’s Ten Types of Innovation
7. McKinsey’s Three Horizons of Growth
8. Customer Journey Map
9. Christensen’s Disruptive Innovation Theory
10. Blue Ocean Strategy
11. Strategyn’s Jobs-To-Be-Done (JTBD) Framework with Job Map
12. Design Sprint Framework
13. The Double Diamond
14. Lean Six Sigma DMAIC
15. TRIZ Problem-Solving Framework
16. Edward de Bono’s Six Thinking Hats
17. Stage-Gate Model
18. Toyota’s Six Steps of Kaizen
19. Microsoft’s Digital Transformation Framework
20. Design for Six Sigma (DFSS)
To download this presentation, visit:
https://www.oeconsulting.com.sg/training-presentations
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Storytelling is an incredibly valuable tool to share data and information. To get the most impact from stories there are a number of key ingredients. These are based on science and human nature. Using these elements in a story you can deliver information impactfully, ensure action and drive change.
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Part 2 Deep Dive: Navigating the 2024 Slowdownjeffkluth1
Introduction
The global retail industry has weathered numerous storms, with the financial crisis of 2008 serving as a poignant reminder of the sector's resilience and adaptability. However, as we navigate the complex landscape of 2024, retailers face a unique set of challenges that demand innovative strategies and a fundamental shift in mindset. This white paper contrasts the impact of the 2008 recession on the retail sector with the current headwinds retailers are grappling with, while offering a comprehensive roadmap for success in this new paradigm.
HR search is critical to a company's success because it ensures the correct people are in place. HR search integrates workforce capabilities with company goals by painstakingly identifying, screening, and employing qualified candidates, supporting innovation, productivity, and growth. Efficient talent acquisition improves teamwork while encouraging collaboration. Also, it reduces turnover, saves money, and ensures consistency. Furthermore, HR search discovers and develops leadership potential, resulting in a strong pipeline of future leaders. Finally, this strategic approach to recruitment enables businesses to respond to market changes, beat competitors, and achieve long-term success.
1. ECO568 - Uncertainty and Financial Markets
Arthur Charpentier and Alfred Galichon
Ecole polytechnique, January 6 2009
1. No-Arbitrage and the Law of One Price
2. General Introduction (1)
Features of Financial Economics
Abundance of …nancial data, empirical testability.
Interactions, collective behavior.
Equilibrium. Partial vs. General: how do you trust your model versus the
market?
3. General Introduction (2)
Rationality
Preferences + beliefs => choices
"Rational" preferences.
- “more” is always preferred to “less” - really?
- Risk-aversion: people buy insurance - but they also purchase lottery
tickets
Rational beliefs: agents’subjective probabilities = objective probabilities
(stationarity; no learning, no insider information, no overcon…dence)
4. General Introduction (3)
S. Ross’"three stylized facts" about …nancial markets:
E¢ cient Markets. Asset returns are unpredictable. Then what is this
course useful for?
Risk Premium. Risky assets have higher expected returns (ie. Lower
prices) than safe ones. By how much?
Correlation. Asset returns are cross-correlated. How to use it?
We shall come up with a consistent theory accounting for these facts.
5. Course outline
Lecture 1 (Jan 6): No Arbitrage and the Law of One Price
Lecture 2 (Jan 13): The Demand for Risk
Lecture 3 (Jan 20): Investment Theory (Static case): MVA, CAPM
Lecture 4 (Jan 21): Informational aspects
Lecture 5 (Feb 10) Investment Theory (Dynamic case, discrete time)
Lecture 6 (Feb 17): Investment Theory (Dynamic case, continuous time)
Lecture 7 (March 3): Term Structure Models
Lecture 8 (March 10): Empirical Puzzles in Asset Pricing
Lecture 9 (March 17): Risk management and Financial bubbles
Exam: March 24
Course webpage: http://groups.google.com/group/x-eco568.
6. Course organization
The class is organized as 1h45 lecture, then 1h45 section ("petite classe").
The lecture slides are distributed in class, and posted online after each lecture.
The "Polycopié de cours" by G. Demange and G. Laroque is avaibable from
the Scolarité. Students are advised to look at it, but the lecture slides are
self-contained.
Oral participation is strongly encouraged!
7. Today’ lecture outline
s
General introduction
No-Arbitrage and the Law of One Price
Section: Arbitrage Pricing Theory, Cox-Ross-Rubinstein
8. The setting
contingent states at time t = 1: ! 2 f1; :::; g.
Examples. ! 2 f0; 1g (no accident/accident); ! value the stock market
at time t = 1.
K assets available at time t = 0: k 2 f1; :::; Kg.
the tableau a! is the value of asset k in contingent state ! , pk price of
k
asset k at time t = 0. A market is the data a! ; pk .
k
Portfolio: combination of assets, z k quantity of asset k. Portfolio price
P k . Portfolio value (t = 1): P a! z k .
(t = 0): k pk z k k
9. Example. Consider the following tableau, where lines correspond to assets,
and columns to states
!
0 1 2 3
a= ;p =
1 1 0 1
what is the value of portfolio of 5 assets k = 1 and 2 asset k = 2 in the state
! = 2?
10. Arbitrage opportunity
De…nition. An arbitrage portfolio is a portfolio z k such that
P ! k P
k ak z 0 for all ! and k pk z k 0, at least one of these E + 1
inequalities being strict.
A market is arbitrage free if there is no arbitrage portfolio.
Proposition. A market a! ; pk without arbitrage opportunity satis…es the
k
Law of One Price:
if for two assets k and l, a! = a! for every state ! , then the assets have the
k l
same price: pk = pl .
0 1 0 1
2 0 1 2
B C B C
Example. Consider a = @1 2 4A ; and p = @1A. The portfolio z =
3 2 5 2
P ! k
( 1; 1; 1) is an arbitrage portfolio, as k ak z = 0 for every ! , and
P k
k pk z = 1.
11. State-price vectors and the
No-Arbitrage theorem
The No-Arbitrage Theorem. A market a! ; pk is arbitrage-free if and only
k
if there is a vector q! such that:
- q! > 0 for every state !
P
- pk = ! a! q! for every asset k
k
q! is then called a state-price vector.
Remark. 1. Although q! is in general not unique, this does not contradict
the law of one price, as every state-price vector q! yields the same set of asset
prices.
2. This notion does not involve the "statistical" probability per se (apart from
its support).
12. 0 1 0 1
2 0 1 1
B C B C
Example. Consider a = @1 2 4A ; and p = @1A. The market is arbitrage-
3 2 5 2
free, and q = (3=7; 0; 1=7) is a state-price vector.
P
Sketch of the proof of the No-Arbitrage theorem. ( is easy: k pk z k =
P P P P
k;! q! a! z k = k;! q! a! z k , thus k a! z k
k k k 0 implies k pk z k
0.
For the converse, we note that the investor is looking for the portfolio with
minimal cost which gets him a positive revenue with certainty in every state of
P P
the world. The investor solves V = inf z k z k pk s.t. k z k a! 0, and V
k
is to be interpreted as the sure gain of the investor. By positive homogeneity,
V = 0 or V = 1, and there is No arbitrage opportunity if and only if
V = 0.
P k P k !
Now, write the Lagrangian V = inf z supq 0 k z pk !;k z ak q! , where
13. q! are the Lagrange multipliers associated to the constraints. But by duality,
P P
one can invert the inf and the sup, and V = supq 0 inf z k z k pk !
! ak q! .
Therefore there is No arbitrage opportunity if and only if there is a vector q
such that
!
X X
inf z k pk a! q!
k =0
z
k !
P
hence ! q! a! = pk for all k. It remains to explain why one can choose
k
q! > 0. Remember, we have introduced the q! as Lagrange multipliers in
the investor’ constrained optimization problem. The null portfolio z = 0 is a
s
solution to the constrained optimization problem which has all the constraints
saturated. By a well-known result on linear programming, all the corresponding
Lagrange multipliers q! can be chosen strictly positive.
Remark: Game-theoretic interpretation. The proof has a game-theoretic
interpretation as a game between Investor and the Market, which sets the state
14. prices in order to minimize the Investor’ gain. The Market’ strategy is to
s s
choose a state-price vector q! , while the Investor’ strategy is to pick up his
s
investment portfolio z k .
The value of this game (for the Market) is then:
!
X X
V = inf sup z k pk a! q!
k
z q 0
k !
V is interpreted as the worse outcome for the Market facing a rational Investor.
This is a zero-sum game: the value of the game for the Investor is V , the
opposite og the value of the game for the Market. The duality principle is
equivalent to a min-max theorem, which precisely says that the value of this
game will be the same regardless whom (of the Investor or the Market) plays
…rst.
15. Consequence: Arrow-Debreu prices
De…nition. An Arrow-Debreu asset is an asset yielding 1 in state ! 0, and 0
otherwise. Denote a!0 = 1f!=!0g.
!
Proposition. If q is a state-price vector, then the price of a!0 is q!0 .
!
Moreover, if there exists a portfolio yielding 1 in state ! 0 and 0 otherwise, then
its price equals q!0 .
Example: Digital options, call options. Suppose a stock price a! can take
up to a …nite number of values v1; :::; vN . Then the digital option of strike vk
is the option d!k = 1fa! =vk g. This is precisely an Arrow-Debreu price.
v
16. Risk neutral probability
Denote k = 0 the riskless asset, ie. a! = 1 for every state ! , and call p0 the
0
price of that asset.
Introduce r the riskfree return r such that 1 + r = p . 1
P P 0
By the law of one price, p0 = ! q! , thus 1 = ! q! (1 + r).
P
Denoting ! = q! (1 + r), one has ! 0 and ! ! = 1, thus ! can be
interpreted as a probability: this is the risk h
neutral probability.
i
1 P ! z k = 1 E P a! z k , where P a! z k is the
One has p = 1+r !;k ! ak 1+r ! k k k k
portfolio contingent value at t = 1.
This probability has no reason to coincide with the "statistical" probability, the
di¤erence comes from the agents risk aversion. More on this soon!
! a!
k
One de…nes rk = pk the return of asset k in state ! . One has for each k,
P !
! ! rk = 1+ r , thus every return have the same risk-neutral probability,
which is the riskless return.
17. Example: Call option. The riskfree asset is a! = 1 + r with unit price, and
0
consider the stock a! with initial price S , where we suppose that the world has
1
only two states, ! = h in which case ah = S (1 + h), and ! = h in which
1
case al = S (1 + l). Suppose (1 + h) S > K > (1 + l) S , and consider the
1
+
call option c! on a1 with strike K . One has c! = a! K , so c! =
1
(1 + h) S K if ! = h, and c! = 0 if ! = l. One looks for the risk-neutral
probability ! . One has l (1 + l)+ h (1 + h) = 1+r, thus h = h l . Thus
r
l
h
the call price is C = 1+r ((1 + h) S r l
K ) = (1+r)(h l) ((1 + h) S K ).
Alternatively, one could also have looked for the value of a replicating portfolio
to hedge the value of the call. Call (z0; z1) such a portfolio; one has
z0 (1 + r) + z1 (1 + h) S = (1 + h) S K
z0 (1 + r ) + z1 (1 + l) S = 0
18. (1+l)[(1+h)S K] (1+h)S K
which solves into z0 = (1+r)(h l)
and z1 = (h l)S . By the law
of one price, the call value equals the initial value of the replicating portfolio,
r l
thus C = (1+r)(h l) ((1 + h) S K ).
19. Complete markets
De…nition. An asset class a! is complete if for every contingent payo¤ c! ,
k
there exists a portfolio z k such that c! = P a! z k .
k k
Proposition. An asset class a! is complete if and only if the rank of the matrix
k
a! is equal to the number of states . In that case, the state-price vector q!
k P
is unique, and a contingent payo¤ c! has price p = ! q! c! .
Important consequences:
1. When the markets are complete, there are at least as many assets than there
are states: K.
2. One can therefore eliminate E redundant assets which are linear com-
binations of independent assets, and suppose in practice that = K .
20. 0 1 0 1
2 0 1 1
B C B C
Example 1. Consider a = @1 2 4A ; and p = @1A. The market is
3 2 5 2
arbitrage-free, but not complete as the …rst two columns sum up to the third
one.
Example 2: options render the market complete. Consider a single asset
a = 5 2 3 with price 2. Consider the market made of a! , and call options
of strike 2 and 3, of payo¤ respectively (a! 2)+ and (a! 3)+.1
0 1 0 The market
5 2 3 1
B C B C
tablean can be written @3 0 1A, and the asset prices are @ p A. Provided
2 0 0 p0
p0 < p < 1, the new market is complete and arbitrage free.
21. Arbitrage bounds*
Proposition. Given an arbitrage-free market M = a! ; pk , de…ne PM the
k
set of probabilities wich are risk-neutral probabilities for this market.
(i) PM is a convex set.
(ii) PM is empty if and only if M o¤ers arbitrage opportunities.
(iii) PM is reduced to a point if and only if the market M is complete.
02P , 0 ? M, P 0 a!
(iv) If and M then that is ! ! k = 0 for all
k.
22. We introduce the notion of replicable claim.
De…nition. Given a contingent claim c! , one says that c! is replicable in the
market M if there exists a portfolio z such that
X
c! = z k a!
k
k
for all ! .
We use the following result to introduce the notion of arbitrage price bounds:
De…nition. For a general contingent claim c! , not necessarily replicable in the
market M , de…ne the lower and upper arbitrage price bounds of the claim as
1 1
v # (c)= # (c) and v " (c) = " (c) , where
1+r 1+r
! ]g and " = 1
# (c) = inf fE ! [c sup fE ! [c! ]g :
2PM 1 + r 2PM
23. We conclude with a result relating the notion of arbitrage price bounds and the
notion of replicability.
Theorem. The claim c! is replicable in the market M if hand only if #i(c) =
" (c). The set of No-Arbitrage prices for c! is given by v # (c) ; v " (c) .
Remark. If the claim c! is not replicable, then adding it to the market with
a price within arbitrage bounds will reduce the set PM : its dimension will
decrease by one.
24. Dynamic arbitrage
In the dynamic case, one observes the evolution of the assets over time, and one
can rebalance one’ portfolio over time. We take the time steps to be discrete.
s
Call a!jt the value of asset a at time t and in state ! , where !jt = ! 0! 1:::! t
(each time step brings on a new piece of randomness). One writes !j (t + 1) =
(!jt; ! t), and we shall suppose there is no uncertainty at date t = 0, namely
! 0 has only one value.
A strategy is the description of a portfolio in the dynamic case, allowing re-
balancing over time: formally a strategy z k (!jt) is the composition of the
investor’ portfolio at time t in the state of the world ! . Note that a strategy
s
can depend on ! 0, ! 1,..., ! t, but not on ! t+k : investors can have memory,
25. but cannot predict the future. The portfolio (liquidation) value at time t is
P k !jt
k z (!jt) ak .
P k !
An arbitrage opportunity is a strategy z such that k z (! 0 ) a k 0 0
P k !jt P k !jt
and k z (!jt 1) ak k z (!jt) ak . The interpretation is that such
strategy has a negative price and allows positive consumption
!jt X !jt !jt
cz = z k (!jt 1) ak z k (!jt) ak 0
k
at each time step.
De…nition. Markets are said to be dynamically complete if for every contingent
!jt
claim c!jt, there exists a portfolio z such that cz = c!jt.
26. Theorem. The three following conditions are equivalent:
(i) There is no arbitrage
P ! P !jt
(ii) There is a vector q!jt > 0 such that k z k (! 0) ak 0 = !jt q!jtcz ,
!jt
where cz is de…ned as above
(iii) For every !jt, there exists a vector q!t+1 (!jt) > 0 such that for all k,
!jt P !jt;! t+1
ak = ! t+1 ak q!t+1 (!jt).
Remark. One sees that q!jt and q!t+1 (!jt) are related by
q!jt+1
q!jt = q!t+1 (!jt) q!t (!jt 1) :::q!1 (!j0), and q!t+1 (!jt) = q .
!jt
27. Reference for the course
Campbell, J., Viceira, L. Strategic Assets Allocation, Oxford.
Demange, G., Laroque, G., Finance et Economie de l’Incertain, Economica.
Ingersoll, J., Theory of Financial Decision Making, Rowman & Little…eld.
Mas-Colell, Whinston, Green, Microeconomic Theory, Oxford.
Ross, S., Neoclassical Finance, Princeton.
Thank you!