Advanced Stochastic Models, Risk Assessment, and Portfolio Optimization The Ideal Risk, Uncertainty, and Performance Measures

, by Rachev, Svetlozar T.; Stoyanov, Stoyan V.; Fabozzi, Frank J.

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ISBN: 9780470053164 | 047005316X
Cover: Hardcover
Copyright: 2/25/2008

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This groundbreaking book extends traditional approaches of risk measurement and portfolio optimization by combining distributional models with risk or performance measures into one framework. Throughout these pages, the expert authors explain the fundamentals of probability metrics, outline new approaches to portfolio optimization, and discuss a variety of essential risk measures. Using numerous examples, they illustrate a range of applications to optimal portfolio choice and risk theory, as well as applications to the area of computational finance that may be useful to financial engineers.

Preface
Acknowledgments About the Authors
Concepts of Probability
Introduction
Basic Concepts
Discrete Probability Distributions
Bernoulli Distribution
Binomial Distribution
Poisson Distribution
Continuous Probability Distributions
Probability Distribution Function, Probability Density Function, and Cumulative Distribution Function
The Normal Distribution
Exponential Distribution
Student's t-distribution
Extreme Value Distribution
Generalized Extreme Value Distribution
Statistical Moments and Quantiles
Location
Dispersion
Asymmetry
Concentration in Tails
Statistical Moments
Quantiles
Sample Moments
Joint Probability Distributions
Conditional Probability
Definition of Joint Probability Distributions
Marginal Distributions
Dependence of Random Variables
Covariance and Correlation
Multivariate Normal Distribution
Elliptical Distributions
Copula Functions
Probabilistic Inequalities
Chebyshev's Inequality
Fr'echet-Hoeffding Inequality
Summary
Optimization
Introduction
Unconstrained Optimization
Minima and Maxima of a Differentiable Function
Convex Functions
Quasiconvex Functions
Constrained Optimization
Lagrange Multipliers
Convex Programming
Linear Programming
Quadratic Programming
Summary
Probability Metrics
Introduction
Measuring Distances: The Discrete Case
Sets of Characteristics
Distribution Functions
Joint Distribution
Primary, Simple, and Compound Metrics
Axiomatic Construction
Primary Metrics
Simple Metrics
Compound Metrics
Minimal and Maximal Metrics
Summary
Technical Appendix
Remarks on the Axiomatic Construction of Probability Metrics
Examples of Probability Distances
Minimal and Maximal Distances
Ideal Probability Metrics
Introduction
The Classical Central Limit Theorem
The Binomial Approximation to the Normal Distribution
The General Case
Estimating the Distance from the Limit Distribution
The Generalized Central Limit Theorem
Stable Distributions
Modeling Financial Assets with Stable Distributions
Construction of Ideal Probability Metrics
Definition
Examples
Summary
Technical Appendix
The CLT Conditions
Remarks on Ideal Metrics
Choice under Uncertainty
Introduction
Expected Utility Theory
St. Petersburg Paradox
The von Neumann-Morgenstern Expected Utility Theory
Types of Utility Functions
Stochastic Dominance
First-Order Stochastic Dominance
Second-Order Stochastic Dominance
Rothschild-Stiglitz Stochastic Dominance
Third-Order Stochastic Dominance
Efficient Sets and the Portfolio Choice Problem
Return versus Payoff
Probability Metrics and Stochastic Dominance
Summary
Technical Appendix
The Axioms of Choice
Stochastic Dominance Relations of Order n
Return versus Payoff and Stochastic
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Advanced Stochastic Models, Risk Assessment, and Portfolio Optimization The Ideal Risk, Uncertainty, and Performance Measures

Summary

Author Biography

Table of Contents

Supplemental Materials