Stochastic optimization models in finance / / editors, W. T. Ziemba, R. G. Vickson

• Record Nr.: UNINA9910786796003321
• Autore: Ziemba W. T.
• Pubbl/distr/stampa: New York : , : Academic Press, , 1975; ©1975
• ISBN: 1-4832-7399-7
• Descrizione fisica: 1 online resource (xvi, 719 pages) : illustrations
• Collana: Economic Theory and Mathematical Economics
• Disciplina: 332.01/51922; 332.0151922
• Soggetti: Finance - Mathematical models; Mathematical optimization; Stochastic processes
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references and index at the end of each chapters.
• Nota di contenuto: 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 and applications; 3. Remarks on pseudo-convex functions; 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 EXERCISES Exercise 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 Choices Involving Risk; 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 Dominance II. 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: The Optimal Stock Mix; Ill Risk Premiums and Other Properties of Stocks Held Long or Short in Optimal Portfolios; IV - Market Prices of Shares Implied by Shareholder Optimization in Purely Competitive Markets Under Idealized Uncertainty
• Sommario/riassunto: Stochastic Optimization Models in Finance