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Introduction　The Fundamental Issues Involved15

Chapter One　The Object of Choice under Uncertainty1

A The Basic Decision-Theoretic Approach1

1．The Ordering of Alternatives1

2．Action Results under Uncertainty4

B Probabilities6

1．Probabilities as Degrees of Confidence6

2．Objective Probability and Real Indeterminateness11

3．The Assessment of Equivalent Objective Probabilities17

3.1．Completely Unknown Probabilities18

3.1.1．The Ellsberg Paradox18

3.1.2．The Axiom of Independence21

3.1.3．A Rehabilitation of the Principle of Insufficient Reason26

3.1.4．Equivalent Probabilities in Tree Diagrams30

3.1.5．Criticism of the Principle of Insufficient Reason33

3.2．Partially Known Probabilities:The Step Theory of Pro-bability35

3.2.1．Completely Known Probability Hierarchies36

3.2.2．Partly Known Probability Hierarchies38

3.3．Result39

Chapter Two　Rational Behavior under Risk41

A The Two-Parametric Substitutive Criteria46

1．Lange's Criterion47

2．The Domar-Musgrave Criterion48

3．The(μ,σ)Criterion50

4．The Mean-Semivariance Criterion51

5．The Criterion of Equivalent Gains and Losses52

5.1．Shackle's Approach52

5.2．The Krelle-Schneider Approach53

6．Limits and Possibilities of the Statistical Criteria55

B The Lexicographic Criterion59

1．The Unconditional Maximization of the Probability of Survi-val59

1.1．The Formal Approach59

1.2．The Problem of the Disaster Level63

2．Aspiration Levels and Saturation Probabilities:A Pragmatic View64

C The Expected-Utility Criterion69

1．The Approach of G.Cramer and D.Bernoulli70

1.1．The Basic Idea70

1.2．Examples72

1.3．An Illustrative Measure of Risk Aversion:The Intensity of Insurance Demand76

1.4．The Problem of Cardinal Utility77

1.5．Specific Risk Preference78

2．The von Neumann-Morgenstern Index79

2.1．The Axioms80

2.2．The Derivation of the Expected-Utility Rule from the Axioms81

D Comparison of Preference Functionals86

1．Expected Utility versus Lexicographic Preference:The Decision for a Decision Criterion86

2．Expected Utility and the Two-Parametric Substitutive Crite-ria:Searching for an Operational Alternative90

2.1．Common Preference Structures90

2.1.1．The Domar-Musgrave Criterion91

2.1.2．The Criterion of Krelle and Schneider92

2.1.3．The(μ,σ)Criterion96

2.1.4．The Mean-Semivariance Criterion99

2.1.5．Result101

2.2．The Local Quadratic Approximation102

2.2.1．The Asymptotic Efficiency of the Variance102

2.2.2．Examples108

2.2.3．The Shape of the Pseudo Indifference Curves in the(μ,σ)Diagram110

2.3．Indifference Curves in the(μ,σ)Diagram for Linear Dis-tribution Classes115

2.4．Conclusions:The(μ,σ)Criterion as Proxy for the Expected-Utility Criterion119

Appendix 1120

Appendix 2122

Chapter Three　The Structure of Risk Preference123

A Psychological Aspects of Risk Evaluation124

1．Psychological Relatively Laws124

1.1．Bernoulli's Relatively Law124

1.2．The Relativity of Stimulus Thresholds127

1.3．The Psychophysical Law130

1.3.1．Fechner's Law130

1.3.2．Stevens's Law132

1.3.3．The Missing Numeraire135

1.3.4．Fechner's Law versus Stevens's Law:The Fmpiri-cal Evidence137

1.3.5．Result144

1.4．The Common Basis:Weber's Relativity Law145

2．Risk Preference and Weber's Relativity Law147

2.1．The Relativity Law and the von Neumann-Morgenstern Function148

2.2．The Relatively Law in the(μ,σ)Diagram153

2.3．Implic？tions for the Intensity of Insurance Demand159

2.3.1．The Influence of Subjective Risk Aversion159

2.3.2．The Influence of Wealth160

2.4．Result162

B The BLOOS Rule163

1．The Complete Preference Ordering under Weak Risk Aver-sion(0<ε<1):The True Reason for Risk Loving164

1.1．The Derived Utility Function for Gross Wealth Distribu-tions164

1.2．Indifference Curves in the(μ.σ)Diagram for Linear Dis-tribution Classes167

1.3．Critique of the Subjectivist Foundation of Risk Prefe-rence175

2．The Complete Indifference-Curve System in the Case of178

Strong Risk Aversion(ε≥1):The Implicit Lexicographic Ordering178

C Arrow's Hypothesis of Increasing Relative and Decreasing Absolute Risk Aversion182

1．The St.Petersburg Paradox184

2．The Utility Boundedness Theorem186

3．The Missing Behavioral Implications of the Utility Bounded-ness Theorem189

Appendix 1195

Appendix 2196

Appendix 3200

Appendix 4204

Chapter Four Multiple Risks207

A Simultaneous Risks208

1．The Law of Large Numbers and the Mean-Value Criterion208

2．The Correlation of Risks210

3．Weber's Relativity Law as the Proper Basis of the Mean-Value Criterion in the Case of Large Numbers212

4．Conclusions219

B Sequential Risks219

1．Optimal Multiperiod Planning of a Pure Investment Program under Uncertainty223

1.1．The Growth Optimum Model223

1.2．The Solution by Means of Stochastic Dynamic Optimiza-tion225

2．Optimal Multiperiod Planning of a Consumption-Investment Program230

2.1．The Multiperiod Preference Functional230

2.1.1．Specific Risk Preference in Multiperiod Planning233

2.1.2．A Preference Functional According to Fechner's Law237

2.2．The Recursive Solution240

2.3．Interpretation of the Solution244

2.3.1．The Rehabilitation of the One-Period Approach244

2.3.2．Time and Risk Aversion246

2.3.3．The Optimal Consumption Strategy250

2.4．Result:The Surprising Simplicity of Multiperiod Plan-ning252

Chapter Five　Areas of Application255

A Portfolio Theory255

1．The Decision Problem255

2．On the Applicability of the(μ,σ)Approach for Portfolio Management258

3．Implications of an Optimal Portfolio Structure261

3.1．The Advantage of Diversification261

3.2．The Age Dependence of the Optimal Portfolio Structure266

3.3．The Wealth Independence of the Optimal Portfolio Structure268

3.3.1．The Apparent Rejection of the Relativity Axiom by the Observation of a Decreasing Velocity of Money Circulation269

3.3.2．A Risk-Theoretic Wealth Effect of a Government Budget Deficit272

4．Summary274

B The Theory ofCurrency Speculation275

1．The Basic Problems of the Spot and Forward Speculators275

1.1．Forward Speculation275

1.2．Spot Market Speculation277

1.3．Interest Arbitrage as the Link Between Spot and Forward Speculation277

1.4．Integrating the Speculation Problem into the Basic Multiperiod Approachv278

2．Optimal Speculation in the Ideal Case280

2.1．The Two-Sided(μ,σ)Diagram280

2.2．The Reaction of the Demand for Forward Currency to Changes in Expectations283

2.2.1．Changes in the Expected Spot Rate284

2.2.2．Changes in the Variance of the Future Spot Rate286

2.3．The Wealth Effect and the Stability Problem286

3．On the Possibility of an Excessively Short Position288

4．Summary294

C Theory of Insurance Demand295

1．Insurance Demand for Given Risks296

1.1．The Basic Calculus of the Insurance Purchaser296

1.2．The Maximum Willingness to Pay for a Full Coverage Insurance Contract299

1.3．The Optimal Degree of Coverage304

1.4．The Age Dependence of Insurance Demand309

2．Insurance and the Size of Risk310

2.1．The Insurance-Induced Substitution Effect under Ideal Conditions311

2.2．Moral Hazard315

2.2.1．Deliberate Destruction of the Object Insured316

2.2.2．The Excess Burden of the Cost-Compensation Principle316

2.2.3．The Optimal Loss Prevention Policy under Com-munity Rating319

2.3．The Allocation of Liability Risks326

2.3.1．The Incentive to Shift Risk326

2.3.2．The Roleofthe Coase Theorem329

2.3.3．The Advantage of Compulsory Insurance331

3．Summary332

List of Abbreviated Journals335

Bibliography337

Author Index351

Subject Index355