From the reviews of the second edition:

"This book is an economics book about stochastic dominance. is certainly a valuable reference for graduate students interested in decision making under uncertainty. It investigates and compares different approaches and presents many examples. Moreover, empirical studies and experimental results play an important role in this book, which makes it interesting to read." (Nicole Bäuerle, Mathematical Reviews, Issue 2007 d)
Book Description

This book is devoted to investment decision-making under uncertainty. The book covers three basic approaches to this process: The stochastic dominance approach; the mean-variance approach; and the non-expected utility approach, focusing on prospect theory and its modified version, cumulative prospect theory.

These approaches are discussed and compared in this book. In addition, this volume examines cases in which stochastic dominance rules coincide with the mean-variance rule and cases in which contradictions between these two approaches may occur. It then discusses the relationship between stochastic dominance rules and prospect theory, and establishes a new investment decision rule which combines the two and which we call prospect stochastic dominance. Although all three approaches are discussed, most of the book is devoted to the stochastic dominance paradigm.

contents

1 On the Measurement of Risk 7
1.1 What is Risk?
1.2 Measures of Risk
a) Domar and Musgrave Risk Indexes
b) Roy's Safety First Rule
c) Dispersion as a Risk Index: Variance and Standard Deviation
d) Semi-variance (SV) as an index of risk
e) Baumol's Risk Measure
f) Value at risk-VaR( a)
g) Shortfall VaR
1.3 Summary
2Expected Utility Theory 25
2.1 Introduction
2.2 Investment Criteria
a) The Maximum Return Criterion (MRC)
b) The Maximum Expected Return Criterion (MERC)
2.3 The Axioms and Proof of the Maximum Expected Utility
Criterion (MEUC)
a) The Payoff of the Investments
b) The Axioms
c) Proof that the Maximum Expected Utility Criterion (MEUC)
is Optimal Decision Rule
2.4 The Properties of Utility Function
a) Preference and Expected Utility
b) Is U(x) a Probability Function or a Utility Function?
2.5 The Meaning of the Utility Units
2.6 MRC, MERC as Special Cases of MEUC
2.7 Utility, Wealth and Change of Wealth
2.8 Summary
viii STOCHASTIC DOMINANCE
3Stochastic Dominance Decision Rules 49
3.1 Partial Ordering: Efficient and Inefficient Sets
a) The Objective Decision
b) The Subjective Decision
3.2 First Degree Stochastic Dominance (FSD)
a) Probability Function, Density Function and Cumulating
Probability Function
b) The FSD Rule
c) The Graphical Exposition of the FSD Rule
d) FSD: A Numerical Example of FSD
e) The Intuitive Explanation of FSD
3.3 Optimal Rule, Sufficient Rules and Necessary Rules for FSD
a) Sufficient Rules
b) Necessary Rules
3.4 Type I and Type II Errors When Sufficient Rules or Necessary
Rules are not Optimal for Investment Screening
3.5 Second Degree Stochastic Dominance (SSD)
a) Risk Aversion
b) The SSD Investment Decision Rule
c) Graphical Exposition of SSD
d) An Intuitive Explanation of SSD
3.6 Sufficient Rules and Necessary Rules for SSD
a) Sufficient Rules
b) Necessary Rules for SSD
3.7 Third Degree Stochastic Dominance (TSD)
a) A Preference for Positive Skewness as a Motivation for TSD
b) The Definition of Skewness
c) Lottery, Insurance and Preference for Positive Skewness
d) Empirical Studies and Positive Skewness Preference (or U'" > 0)
e) Decreasing Absolute Risk Aversion (DARA), and Positive
Skewness Preferences (or U'" > 0)
f) The Optimal Investment Rule for U G U3: TSD
g) Graphical Exposition of TSD
h) The Intuitive Explanation of TSD
3.8 Sufficient Rules and Necessary Rules for U G U3
a) Sufficient Rules
b) Necessary Rules for TSD
3.9 Decreasing Absolute Risk Aversion (DARA) Stochastic
Dominance (DSD)
a) DARA Utility Functions
b) DSD with Equal Mean Distributions
TABLE OF CONTENTS
3.10 Risk-seeking Stochastic Dominance (RSSD)
a) Risk-seeking Stochastic Dominance (RSSD)
b) Graphical Exposition of SSD
c) The Relationship Between SSD and SSD
d) The Relationship Between FSD, SSD and SSD
3.11 n^^ Order Stochastic Dominance
3.12 Stochastic Dominance Rules: Extension to Discrete Distributions
3.13 The Role of the Mean and Variance in Stochastic Dominance Rules
3.14 Summary
4Stochastic Dominance: The Quantile 143
4.1 The Distribution Quantile
4.2 Stochastic Dominance Rules Stated in Terms of Distribution
Quantiles
a) The FSD Rule with Quantiles
b) The SSD Rule with Quantiles
4.3 Stochastic Dominance Rules with a Riskless Asset: A Perfect
Capital Market
a) FSD with a Riskless Asset: The FSDR Rule
b) Graphical Illustration of the FSDR Rule
c) SSD with a Riskless Asset: The SSDR Rule
d) The SD and SDR Efficient Sets
4.4 Stochastic Dominance Rules with a Riskless Asset: An Imperfect
Capital Market
4.5 Summary
5Algorithms for Stochastic Dominance 173
5.1 Using the Necessary Conditions and Transitivity to Reduce the
Number of Comparisons
5.2 The FSD Algorithm
5.3 The SSD Algorithm
5.4 The TSD Algorithm
5.5 A Numerical Example Showing the Flaw In Existing TSD Algorithm
5.6 The Empirical Results
5.7 The SDR Algorithms
a) FSDR Algorithm
b) SSDR Algorithm
5.8 Summary
STOCHASTIC DOMINANCE
6Stochastic Dominance with Specific Distributions 197
6.1 Normal Distributions
a) Properties of the Normal Distribution
b) Dominance Without a Riskless Asset
c) Dominance With a Riskless Asset
6.2 Lognormal Distributions
a) Properties of the Lognormal Distribution
b) Dominance Without a Riskless Asset
c) Dominance With a Riskless Asset
6.3 Truncated Normal Distributions
a) Symmetrical Truncation
b) Non-symmetrical Truncation
6.4 Distributions that Intercept Once at Most
6.5 Summary
7The Empirical Studies 223
7.1 The Effectiveness of the Various Decision Rules: A Perfect
Market
7.2 The Effectiveness of the Various Decision Rules: An Imperfect
Market
7.3 The Performance of Mutual Funds with Transaction Costs
7.4 Further Reduction in the Efficient Sets: Convex Stochastic Dominance
(CSD)
7.5 Sampling Errors: Statistical Limitations of the Empirical Studies
7.6 Summary
8Applications of Stochastic Dominance Rules 241
8.1 Capital Structure and the Value of the Firm
8.2 Production, Saving and Diversification
8.3 Estimating the Probability of Bankruptcy
8.4 Option Evaluation, Insurance Premium and Portfolio Insurance
8.5 Application of SD Rules in Agricultural Economics
8.6 Application of SD Rules in Medicine
8.7 Measuring Income Inequity
8.8 Application of SD Rules in the Selection of Parameter
Estimators
8.9 Summary
TABLE OF CONTENTS xi
9Stochastic Dominance and Risk Measures 257
9.1 When is One Investment Riskier Than Another Investment?
9.2 Mean Preserving Spread (MPS)
9.3 Unequal Means and "Riskier Than" with the Riskless Asset
9.4 "Riskier Than" and DARA Utility Function: Mean Preserving
Anti spread
9.5 Summary
10Stochastic Dominance and Diversification 271
10.1 Arrow's Condition for Diversification
a) Diversification Between a Risky and a Riskless Asset
b) The Effect of Shifts in Parameters on Diversification
10.2 Extension of the SD Analyses to the Case of Two-Risky Assets
10.3 Diversification and Expected Utility: Some Common Utility
Functions
a) Shift in r
b) Shift in x
c) MPS Shifts
d) MPA Shifts
e) MPSA Shifts
10.4 Summary
11Decision Making and the Investment Horizon 293
11.1 Tobin's M-V Multi-Period Analysis
11.2 Sharpe's Re ward-to-Variability Ratio and the Investment
Horizon
11.3 The Effect of the Investment Horizon on Correlations
11.4 The Effect of the Investment Horizon on the Composition
of M-V Portfolios
11.5 The Effect of the Investment Horizon on Beta
11.6 Stochastic Dominance and the Investment Horizon
11.7 Contrasting The Size of the M-V and SD Efficient Set
11.8 Summary
xii STOCHASTIC DOMINANCE
12The CAPM and Stochastic Dominance 313
12.1 The CAPM with Heterogeneous Investment Horizon
a) Quadratic Utility Function
b) Single-Period Normal Distributions
c) Multiperiod Normal Distributions
d) Lognormal Distributions
12.2 Summary
13Almost Stochastic Dominance (ASD) 331
13.1 The Possible Paradoxes
13.2 FSD* Criterion Corresponding to U *.
13.3 SSD* Criterion Corresponding to U 2 .
13.4 Application of FSD* To Investment Choices: Stocks Versus Bonds
13.5 ASD: Experimental Results
13.6 Summary
14Non-Expected Utility and Stochastic Dominance 353
14.1 The Allais Paradox
14.2 Non-Expected Utility Theory
14.3 Decision Weights and FSD Violation
14.4 Temporary and Permanent Attitude Toward Risk
14.5 Summary
15Stochastic Dominance and Prospect Theory 373
15.1 CPT and FSD Rule
15.2 Prospect Stochastic Dominance (PSD)
15.3 Markowitz's Stochastic Dominance
15.4 CPT, M-V And The CAPM
15.5 Testing the Competing Theories: SD Approach
a) Testing the Competing Theories: SD Approach
b) The Stochastic Dominance Approach
c) Are People Risk Averse? (SSD)
d) Is CPT Valid Theory? (PSD)
15.6 SSD, PSD, MSD and the Efficiency of the Market Portfolio
15.7 Summary
Future Research 395
Bibliography 407
Index 431