1st Edition

Stochastic Dominance and Applications to Finance, Risk and Economics

    456 Pages
    by Chapman & Hall

    456 Pages
    by Chapman & Hall

    Drawing from many sources in the literature, Stochastic Dominance and Applications to Finance, Risk and Economics illustrates how stochastic dominance (SD) can be used as a method for risk assessment in decision making. It provides basic background on SD for various areas of applications.

    Useful Concepts and Techniques for Economics Applications

    The majority of the text presents a systematic exposition of SD, emphasizing rigor and generality. It covers utility theory, multivariate SD, quantile functions, risk modeling, Choquet integrals, other risk measures, statistical inference, nonparametric estimation, hypothesis testing, and econometrics. The remainder of the book explores new applications of SD in finance, risk, and economics. At the beginning of each economic concept, the authors clearly explain only the necessary mathematics so readers are not overburdened with learning nonessential, arduous mathematics.

    This accessible guide helps readers build a useful repertoire of mathematical tools in decision making under uncertainty, especially in investment science. It provides thorough coverage on the theory of SD, along with many applications to economics and other fields where risk is crucial.

    Utility in Decision Theory

    Choice under certainty

    Basic probability background

    Choice under uncertainty

    Utilities and risk attitudes

    Foundations of Stochastic Dominance

    Some preliminary mathematics

    Deriving representations of preferences

    Stochastic dominance (SD)

    Issues in Stochastic Dominance

    A closer look at the mean-variance rule

    Multivariate SD

    Stochastic dominance via quantile functions

    Financial Risk Measures

    The problem of risk modeling

    Some popular risk measures

    Desirable properties of risk measures

    Choquet Integrals as Risk Measures

    Extended theory of measures

    Capacities

    The Choquet integral

    Basic properties of the Choquet integral

    Comonotonicity

    Notes on copulas

    A characterization theorem

    A class of coherent risk measures

    Consistency with SD

    Foundational Statistics for Stochastic Dominance

    From theory to applications

    Structure of statistical inference

    Generalities on statistical estimation

    Nonparametric estimation

    Basics of hypothesis testing

    Models and Data in Econometrics

    Justifications of models

    Coarse data

    Modeling dependence structure

    Some additional statistical tools

    Applications to Finance

    Diversification

    Diversification on convex combinations

    Prospect and Markowitz SD

    Market rationality and efficiency

    SD and rationality of momentum effect

    Applications to Risk Management

    Measures of profit/loss for risk analysis

    REITs and stocks and fixed-income assets

    Evaluating hedge funds performance

    Evaluating iShare performance

    Applications to Economics

    Indifference curves/location-scale (LS) family

    LS family for n random seed sources

    Elasticity of risk aversion and trade

    Income inequality

    Appendix: Stochastic Dominance Tests

    Bibliography

    Index

    Exercises appear at the end of each chapter.

    Biography

    Songsak Sriboonchitta is an associate professor and dean of the Faculty of Economics at Chiang Mai University in Thailand.

    Wing-Keung Wong is a professor of economics at Hong Kong Baptist University in China.

    Sompong Dhompongsa is a professor of mathematics at Chiang Mai University in Thailand.

    Hung T. Nguyen is a professor of mathematical sciences at New Mexico State University in Las Cruces.

    The book helps readers in building a useful repertoire of mathematical tools in decision making under uncertainty, especially in investment science, and provides thorough coverage on the theory of SD, along with many applications to economics and other fields where risk is crucial. Given these, it may be used as a textbook for a course on stochastic dominance for beginners as well as a solid reference book for researchers, especially in the field of economics.
    Zentralblatt MATH 1180