Stochastic Optimization Models in Finance

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Front Cover; Stochastic Optimization Models in Finance; Copyright Page; Dedication; Table of Contents; PREFACE; ACKNOWLEDGMENTS; Part I: Mathematical Tools; INTRODUCTION; I. Expected Utility Theory; II. Convexity and the Kuhn-Tucker Conditions; III. Dynamic Programming; SECTION1: EXPECTED UTILITY THEORY; CHAPTER 1. A GENERAL THEORY OF SUBJECTIVE PROBABILITIESAND EXPECTED UTILITIES; 1.Introduction; 2. Definitions andnotation; 3. Axioms and summarytheorem; 4.Theorems; 5. Proof of Theorem3; 6. Proof of Theorem4; SECTION2: CONVEXITY AND THE KUHN-TUCKERCONDITIONS; CHAPTER2. PSEUDO-CONVEX FUNCTIONS

Abstract1.Introduction; 2. Properties of pseudo-convex functions andapplications; 3. Remarks on pseudo-convexfunctions; 4.Acknowledgement; CHAPTER3. CONVEXITY, PSEUDO-CONVEXITY AND QUASI-CONVEXITY OF COMPOSITE FUNCTIONS; ABSTRACT; Preliminaries; Principal result; Applications; SECTION3: DYNAMIC PROGRAMMING; Chapter4. Introduction to Dynamic Programming; I. Introduction; II. Sequential Decision Processes; III. Terminating Process; IV. The Main Theorem and an Algorithm; V. Nonterminating Processes; ACKNOWLEDGMENT; REFERENCES; CHAPTER5. COMPUTATIONAL AND REVIEW EXERCISES; Exercise Source Notes

CHAPTER6. MIND-EXPANDING EXERCISESExercise Source Notes; Part II: Qualitative Economic Results; INTRODUCTION; I. Stochastic Dominance; II. Measures of Risk Aversion; III. Separation Theorems; IV. Additional Reading Material; SECTION1: STOCHASTIC DOMINANCE; Chapter 1. The Efficiency Analysis of ChoicesInvolvingRisk; I. INTRODUCTION; II. UNRESTRICTED UTILITY-THE GENERALEFFICIENCY CRITERION; III. EFFICIENCY IN THE FACE OF RISK AVERSION; IV. THE LIMITATIONS OF THE MEAN-VARIANCEEFFICIENCY CRITERION; V. CONCLUSION; REFERENCES; Chapter 2. A Unified Approach to Stochastic Dominance

I. Introduction to Stochastic DominanceII. Examples of Stochastic Dominance Relations; III. Probabilistic Content of Stochastic Dominance; REFERENCES; SECTION2: MEASURES OF RISK AVERSION; CHAPTER3. RISK AVERSION IN THE SMALL AND IN THE LARGE; 1. SUMMARY AND INTRODUCTION; 2. THE RISK PREMIUM; 3. LOCAL RISK AVERSION; 4. CONCAVITY; 5. COMPARATIVE RISK AVERSION; 6. CONSTANT RISK AVERSION; 7. INCREASING AND DECREASING RISK AVERSION; 8. OPERATIONS WHICH PRESERVE DECREASING RISK AVERSION; 9. EXAMPLES; 10. PROPORTIONAL RISK AVERSION; 11. CONSTANT PROPORTIONAL RISK AVERSION

12. INCREASING AND DECREASING PROPORTIONAL RISK AVERSION13. RELATED WORK OF ARROW; ADDENDUM; SECTION3: SEPARATION THEOREMS; CHAPTER 4. THE VALUATION OF RISK ASSETS AND THE SELECTION OF RISKY INVESTMENTS IN STOCKPORTFOLIOS AND CAPITAL BUDGETS; Introduction and Preview of Some Conclusions; I - Portfolio Selection for an Individual Investor:The Separation Theorem; II -Portfolio Selection: TheOptimal Stock Mix; Ill Risk Premiums and Other Properties of Stocks Held Long or Shortin Optimal Portfolios

IV - Market Prices of Shares Implied by Shareholder Optimization in Purely Competitive MarketsUnder Idealized Uncertainty

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