Introduction The Fundamental Issues Involved 15
Chapter One The Object of Choice under Uncertainty 1
A The Basic Decision-Theoretic Approach 1
1．The Ordering of Alternatives 1
2．Action Results under Uncertainty 4
B Probabilities 6
1．Probabilities as Degrees of Confidence 6
2．Objective Probability and Real Indeterminateness 11
3．The Assessment of Equivalent Objective Probabilities 17
3.1．Completely Unknown Probabilities 18
3.1.1．The Ellsberg Paradox 18
3.1.2．The Axiom of Independence 21
3.1.3．A Rehabilitation of the Principle of Insufficient Reason 26
3.1.4．Equivalent Probabilities in Tree Diagrams 30
3.1.5．Criticism of the Principle of Insufficient Reason 33
3.2．Partially Known Probabilities:The Step Theory of Pro-bability 35
3.2.1．Completely Known Probability Hierarchies 36
3.2.2．Partly Known Probability Hierarchies 38
3.3．Result 39
Chapter Two Rational Behavior under Risk 41
A The Two-Parametric Substitutive Criteria 46
1．Lange's Criterion 47
2．The Domar-Musgrave Criterion 48
3．The(μ,σ)Criterion 50
4．The Mean-Semivariance Criterion 51
5．The Criterion of Equivalent Gains and Losses 52
5.1．Shackle's Approach 52
5.2．The Krelle-Schneider Approach 53
6．Limits and Possibilities of the Statistical Criteria 55
B The Lexicographic Criterion 59
1．The Unconditional Maximization of the Probability of Survi-val 59
1.1．The Formal Approach 59
1.2．The Problem of the Disaster Level 63
2．Aspiration Levels and Saturation Probabilities:A Pragmatic View 64
C The Expected-Utility Criterion 69
1．The Approach of G.Cramer and D.Bernoulli 70
1.1．The Basic Idea 70
1.2．Examples 72
1.3．An Illustrative Measure of Risk Aversion:The Intensity of Insurance Demand 76
1.4．The Problem of Cardinal Utility 77
1.5．Specific Risk Preference 78
2．The von Neumann-Morgenstern Index 79
2.1．The Axioms 80
2.2．The Derivation of the Expected-Utility Rule from the Axioms 81
D Comparison of Preference Functionals 86
1．Expected Utility versus Lexicographic Preference:The Decision for a Decision Criterion 86
2．Expected Utility and the Two-Parametric Substitutive Crite-ria:Searching for an Operational Alternative 90
2.1．Common Preference Structures 90
2.1.1．The Domar-Musgrave Criterion 91
2.1.2．The Criterion of Krelle and Schneider 92
2.1.3．The(μ,σ)Criterion 96
2.1.4．The Mean-Semivariance Criterion 99
2.1.5．Result 101
2.2．The Local Quadratic Approximation 102
2.2.1．The Asymptotic Efficiency of the Variance 102
2.2.2．Examples 108
2.2.3．The Shape of the Pseudo Indifference Curves in the(μ,σ)Diagram 110
2.3．Indifference Curves in the(μ,σ)Diagram for Linear Dis-tribution Classes 115
2.4．Conclusions:The(μ,σ)Criterion as Proxy for the Expected-Utility Criterion 119
Appendix 1 120
Appendix 2 122
Chapter Three The Structure of Risk Preference 123
A Psychological Aspects of Risk Evaluation 124
1．Psychological Relatively Laws 124
1.1．Bernoulli's Relatively Law 124
1.2．The Relativity of Stimulus Thresholds 127
1.3．The Psychophysical Law 130
1.3.1．Fechner's Law 130
1.3.2．Stevens's Law 132
1.3.3．The Missing Numeraire 135
1.3.4．Fechner's Law versus Stevens's Law:The Fmpiri-cal Evidence 137
1.3.5．Result 144
1.4．The Common Basis:Weber's Relativity Law 145
2．Risk Preference and Weber's Relativity Law 147
2.1．The Relativity Law and the von Neumann-Morgenstern Function 148
2.2．The Relatively Law in the(μ,σ)Diagram 153
2.3．Implic？tions for the Intensity of Insurance Demand 159
2.3.1．The Influence of Subjective Risk Aversion 159
2.3.2．The Influence of Wealth 160
2.4．Result 162
B The BLOOS Rule 163
1．The Complete Preference Ordering under Weak Risk Aver-sion(0<ε<1):The True Reason for Risk Loving 164
1.1．The Derived Utility Function for Gross Wealth Distribu-tions 164
1.2．Indifference Curves in the(μ.σ)Diagram for Linear Dis-tribution Classes 167
1.3．Critique of the Subjectivist Foundation of Risk Prefe-rence 175
2．The Complete Indifference-Curve System in the Case of 178
Strong Risk Aversion(ε≥1):The Implicit Lexicographic Ordering 178
C Arrow's Hypothesis of Increasing Relative and Decreasing Absolute Risk Aversion 182
1．The St.Petersburg Paradox 184
2．The Utility Boundedness Theorem 186
3．The Missing Behavioral Implications of the Utility Bounded-ness Theorem 189
Appendix 1 195
Appendix 2 196
Appendix 3 200
Appendix 4 204
Chapter Four Multiple Risks 207
A Simultaneous Risks 208
1．The Law of Large Numbers and the Mean-Value Criterion 208
2．The Correlation of Risks 210
3．Weber's Relativity Law as the Proper Basis of the Mean-Value Criterion in the Case of Large Numbers 212
4．Conclusions 219
B Sequential Risks 219
1．Optimal Multiperiod Planning of a Pure Investment Program under Uncertainty 223
1.1．The Growth Optimum Model 223
1.2．The Solution by Means of Stochastic Dynamic Optimiza-tion 225
2．Optimal Multiperiod Planning of a Consumption-Investment Program 230
2.1．The Multiperiod Preference Functional 230
2.1.1．Specific Risk Preference in Multiperiod Planning 233
2.1.2．A Preference Functional According to Fechner's Law 237
2.2．The Recursive Solution 240
2.3．Interpretation of the Solution 244
2.3.1．The Rehabilitation of the One-Period Approach 244
2.3.2．Time and Risk Aversion 246
2.3.3．The Optimal Consumption Strategy 250
2.4．Result:The Surprising Simplicity of Multiperiod Plan-ning 252
Chapter Five Areas of Application 255
A Portfolio Theory 255
1．The Decision Problem 255
2．On the Applicability of the(μ,σ)Approach for Portfolio Management 258
3．Implications of an Optimal Portfolio Structure 261
3.1．The Advantage of Diversification 261
3.2．The Age Dependence of the Optimal Portfolio Structure 266
3.3．The Wealth Independence of the Optimal Portfolio Structure 268
3.3.1．The Apparent Rejection of the Relativity Axiom by the Observation of a Decreasing Velocity of Money Circulation 269
3.3.2．A Risk-Theoretic Wealth Effect of a Government Budget Deficit 272
4．Summary 274
B The Theory ofCurrency Speculation 275
1．The Basic Problems of the Spot and Forward Speculators 275
1.1．Forward Speculation 275
1.2．Spot Market Speculation 277
1.3．Interest Arbitrage as the Link Between Spot and Forward Speculation 277
1.4．Integrating the Speculation Problem into the Basic Multiperiod Approachv 278
2．Optimal Speculation in the Ideal Case 280
2.1．The Two-Sided(μ,σ)Diagram 280
2.2．The Reaction of the Demand for Forward Currency to Changes in Expectations 283
2.2.1．Changes in the Expected Spot Rate 284
2.2.2．Changes in the Variance of the Future Spot Rate 286
2.3．The Wealth Effect and the Stability Problem 286
3．On the Possibility of an Excessively Short Position 288
4．Summary 294
C Theory of Insurance Demand 295
1．Insurance Demand for Given Risks 296
1.1．The Basic Calculus of the Insurance Purchaser 296
1.2．The Maximum Willingness to Pay for a Full Coverage Insurance Contract 299
1.3．The Optimal Degree of Coverage 304
1.4．The Age Dependence of Insurance Demand 309
2．Insurance and the Size of Risk 310
2.1．The Insurance-Induced Substitution Effect under Ideal Conditions 311
2.2．Moral Hazard 315
2.2.1．Deliberate Destruction of the Object Insured 316
2.2.2．The Excess Burden of the Cost-Compensation Principle 316
2.2.3．The Optimal Loss Prevention Policy under Com-munity Rating 319
2.3．The Allocation of Liability Risks 326
2.3.1．The Incentive to Shift Risk 326
2.3.2．The Roleofthe Coase Theorem 329
2.3.3．The Advantage of Compulsory Insurance 331
3．Summary 332
List of Abbreviated Journals 335
Bibliography 337
Author Index 351
Subject Index 355