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Stochastic Optimization Models in Finance
- 1st Edition - May 12, 2014
- Editors: W. T. Ziemba, R. G. Vickson
- Language: English
- Paperback ISBN:9 7 8 - 1 - 4 8 3 2 - 4 8 8 1 - 3
- eBook ISBN:9 7 8 - 1 - 4 8 3 2 - 7 3 9 9 - 0
Stochastic Optimization Models in Finance focuses on the applications of stochastic optimization models in finance, with emphasis on results and methods that can and have been… Read more
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Request a sales quoteStochastic Optimization Models in Finance focuses on the applications of stochastic optimization models in finance, with emphasis on results and methods that can and have been utilized in the analysis of real financial problems. The discussions are organized around five themes: mathematical tools; qualitative economic results; static portfolio selection models; dynamic models that are reducible to static models; and dynamic models. This volume consists of five parts and begins with an overview of expected utility theory, followed by an analysis of convexity and the Kuhn-Tucker conditions. The reader is then introduced to dynamic programming; stochastic dominance; and measures of risk aversion. Subsequent chapters deal with separation theorems; existence and diversification of optimal portfolio policies; effects of taxes on risk taking; and two-period consumption models and portfolio revision. The book also describes models of optimal capital accumulation and portfolio selection. This monograph will be of value to mathematicians and economists as well as to those interested in economic theory and mathematical economics.
Preface
Acknowledgments
Part I. Mathematical Tools
Introduction
1. Expected Utility Theory
A General Theory of Subjective Probabilities and Expected Utilities
2. Convexity and the Kuhn-Tucker Conditions
Pseudo-Convex Functions
Convexity, Pseudo-Convexity and Quasi-Convexity of Composite Functions
3. Dynamic Programming
Introduction to Dynamic Programming
Computational and Review Exercises
Mind-Expanding Exercises
Part II. Qualitative Economic Results
Introduction
1. Stochastic Dominance
The Efficiency Analysis of Choices Involving Risk
A Unified Approach to Stochastic Dominance
2. Measures of Risk Aversion
Risk Aversion in the Small and in the Large
3. Separation Theorems
The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets
Separation in Portfolio Analysis
Computational and Review Exercises
Mind-Expanding Exercises
Part III. Static Portfolio Selection Models
Introduction
1. Mean-Variance and Safety First Approaches and Their Extensions
The Fundamental Approximation Theorem of Portfolio Analysis in Terms of Means, Variances and Higher Moments
The Asymptotic Validity of Quadratic Utility as the Trading Interval Approaches
Safety-First and Expected Utility Maximization in Mean-Standard Deviation Portfolio Analysis
Choosing Investment Portfolios When the Returns have Stable Distributions
2. Existence and Diversification of Optimal Portfolio Policies
On the Existence of Optimal Policies Under Uncertainty
General Proof That Diversification Pays
3. Effects of Taxes on Risk Taking
The Effects of Income, Wealth, and Capital Gains Taxation on Risk-Taking
Some Effects of Taxes on Risk-Taking
Computational and Review Exercises
Mind-Expanding Exercises
Part IV. Dynamic Models Reducible to Static Models
Introduction
1. Models that have a Single Decision Point
Investment Analysis Under Uncertainty
2. Risk Aversion Over Time Implies Static Risk Aversion
Multiperiod Consumption-Investment Decisions
3. Myopic Portfolio Policies
On Optimal Myopic Portfolio Policies, with and without Serial Correlation of Yields
Computational and Review Exercises
Mind-Expanding Exercises
Part V. Dynamic Models
Introduction
Appendix A. An Intuitive Outline of Stochastic Differential Equations and Stochastic Optimal Control
1. Two-Period Consumption Models and Portfolio Revision
Consumption Decisions Under Uncertainty
A Dynamic Model for Bond Portfolio Management
2. Models of Optimal Capital Accumulation and Portfolio Selection
Multiperiod Consumption-Investment Decisions and Risk Preference
Lifetime Portfolio Selection by Dynamic Stochastic Programming
Optimal Investment and Consumption Strategies Under Risk for a Class of Utility Functions
3. Models of Option Strategy
The Value of the Call Option on a Bond
Evaluating a Call Option and Optimal Timing Strategy in the Stock Market
Bond Refunding with Stochastic Interest Rates
Minimax Policies for Selling an Asset and Dollar Averaging
4. The Capital Growth Criterion and Continuous-Time Models
Investment Policies for Expanding Businesses Optimal in a Long-Run Sense
Portfolio Choice and the Kelly Criterion
Optimum Consumption and Portfolio Rules in a Continuous-Time Model
Computational and Review Exercises
Mind-Expanding Exercises
Bibliography
Index
- No. of pages: 736
- Language: English
- Edition: 1
- Published: May 12, 2014
- Imprint: Academic Press
- Paperback ISBN: 9781483248813
- eBook ISBN: 9781483273990
WZ
W. T. Ziemba
Affiliations and expertise
University of British ColumbiaRead Stochastic Optimization Models in Finance on ScienceDirect