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.
Table of Contents
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
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
The Choquet integral
Basic properties of the Choquet integral
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
Basics of hypothesis testing
Models and Data in Econometrics
Justifications of models
Modeling dependence structure
Some additional statistical tools
Applications to Finance
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
Appendix: Stochastic Dominance Tests
Exercises appear at the end of each chapter.
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