Introduction 3
1. Expected Utility Theory 11
A General Theory of Subjective Probabilities and Expected Utilities
Peter C. Fishburn
The Annals of Mathematical Statistics 40, 1419-1429 (1969) /1
2. Convexity and the Kuhn Tucker Conditions 23
Pseudo-Convex Functions
O. L. Mangasarian
Journal ofSIAM Control A3, 281-290 (1965) 23
Convexity, Pseudo-Convexity and Quasi-Con vexity of Composite Functions
O. L. Mangasarian
Cahiers du Centre d'Etudes de Recherche Operationelle
12,114-122(1970) 33
3. Dynamic Programming 43
Introduction to Dynamic Programming
W. T. Ziemba 43
Computational and Review Exercises 57
Mind-Expanding Exercises 67
PART II. QUALITATIVE ECONOMIC RESULTS
Introduction 81
1. Stochastic Dominance 89
The Efficiency Analysis of Choices Involving Risk
G. Hanoch and H. Levy
The Review of Economic Studies 36, 335-346 (1969) 89
A Unified Approach to Stochastic Dominance
S. L. Brumelle and R. G. Vickson 101
2. Measures of Risk Aversion 115
Risk Aversion in the Small and in the Large
John W. Pratt
Econometrica 32, 122-136 (1964) 115
3. Separation Theorems 131
The Valuation of Risk Assets and the Selection of Risky Investments
in Stock Portfolios and Capital Budgets
John Lintner
The Review of Economics and Statistics 47, 13-37 (1965) 131
Separation in Portfolio Analysis
R. G. Vickson 157
Computational and Review Exercises 171
Mind-Expanding Exercises 183
PART III. STATIC PORTFOLIO SELECTION MODELS
Introduction 203
1. Mean-Variance and Safety First Approaches and Their Extensions 215
The Fundamental Approximation Theorem of Portfolio Analysis
in Terms of Means, Variances and Higher Moments
Paul A. Samuelson
The Review of Economic Studies 37, 537-542 (1970) 215
The Asymptotic Validity of Quadratic Utility as the Trading Interval
Approaches Zero
James A. Ohlson 221
vm CONTENTS
Safety-First and Expected Utility Maximization in Mean-Standard
Deviation Portfolio Analysis
David H. Pyle and Stephen J. Turnovsky
The Review of Economics and Statistics 52, 75-81 (1970) 235
Choosing Investment Portfolios When the Returns Have Stable Distributions
W. T. Ziemba
"Mathematical Programming in Theory and Practice," P. L. Hammer
and G. Zoutendijk, eds., pp. 443-482. North-Holland, Amsterdam
(1974) 243
2. Existence and Diversification of Optimal Portfolio Policies 267
On the Existence of Optimal Policies under Uncertainty
Hayne E. Leland
Journal of Economic Theory 4, 35-44 (1972) 267
General Proof That Diversification Pays
Paul A. Samuelson
Journal of Financial and Quantitative Analysis 2, 1-13(1967) 277
3. Effects of Taxes on Risk Taking 291
The Effects of Income, Wealth, and Capital Gains Taxation on Risk-Taking
J. E. Stiglitz
Quarterly Journal of Economics 83, 263-283 (1967) 291
Some Effects of Taxes on Risk-Taking
B. Naslund
The Review of Economic Studies 35, 289-306 (1968) 313
Computational and Review Exercises 331
Mind-Expanding Exercises 343
PART IV. DYNAMIC MODELS REDUCIBLE TO STATIC MODELS
Introduction 367
1. Models That Have a Single Decision Point 373
Investment Analysis under Uncertainty
Robert Wilson
Management Science 15, B-650-B-664 (1969) 3 73
CONTENTS IX
2. Risk Aversion over Time Implies Static Risk Aversion 389
Multiperiod Consumption-Investment Decisions
Eugene F. Fama
The American Economic Review 60, 163-174 (1970) 389
3. Myopic Portfolio Policies 401
On Optimal Myopic Portfolio Policies, with and without Serial Correlation
of Yields
Nils H. Hakansson
The Journal of Business of the University of Chicago 44, 324-334 (1971) 401
Computational and Review Exercises 413
Mind-Expanding Exercises 417
PART V. DYNAMIC MODELS
Introduction 429
Appendix A. An Intuitive Outline of Stochastic Differential Equations and
Stochastic Optimal Control
R. G. Vickson 453
1. Two-Period Consumption Models and Portfolio Revision 459
Consumption Decisions under Uncertainty
Jacques H. Dreze and Franco Modigliani
Journal of Economic Theory 5, 308-335 (1972) 459
A Dynamic Model for Bond Portfolio Management
Stephen P. Bradley and Dwight B. Crane
Management Science 19, 139-151 (1972) 487
2. Models of Optimal Capital Accumulation and Portfolio Selection 501
Multiperiod Consumption-Investment Decisions and Risk Preference
Edwin H. Neave
Journal of Economic Theory 3, 40-53 (1971) 501
Lifetime Portfolio Selection by Dynamic Stochastic Programming
Paul A. Samuelson
The Review of Economics and Statistics 51, 239-246 (1969) 517
x CONTENTS
Optimal Investment and Consumption Strategies under Risk for a Class
of Utility Functions
Nils H. Hakansson
Econometrica 38, 587-607 (1970) 525
3. Models of Option Strategy 547
The Value of the Call Option on a Bond
Gordon Pye
Journal of Political Economy 74, 200-205 (1966) 547
Evaluating a Call Option and Optimal Timing Strategy in the Stock Market
Howard M. Taylor
Management Science 14, 111-120 (1967) 553
Bond Refunding with Stochastic Interest Rates
Basil A. Kalymon
Management Science 18, 171-183 (1971) 563
Minimax Policies for Selling an Asset and Dollar Averaging
Gordon Pye
Management Science 17, 379-393 (1971) 577
4. The Capital Growth Criterion and Continuous-Time Models 593
Investment Policies for Expanding Businesses Optimal in a Long-Run Sense
Leo Breiman
Naval Research Logistics Quarterly 7, 647-651 (1960) 593
Portfolio Choice and the Kelly Criterion
Edward O. Thorp 599
Business and Economics Statistics Section. Proceedings of the American
Statistical Association 215-224 (1971).
Optimum Consumption and Portfolio Rules in a Continuous-Time Model
Robert C. Merton
Journal of Economic Theory 3, 373^113 (1971) 621
Computational and Review Exercises 663
Mind-Expanding Exercises 677
Bibliography 701
Index 715
CONTENTS