Advanced Stochastic Models, Risk Assessment, and Portfolio Optimization: The

Advanced Stochastic Models, Risk Assessment, and Portfolio Optimization The finance industry is seeing increased interest in new risk measures and techniques for portfolio optimization when parameters of the model are uncertain. This groundbreaking book extends traditional approaches of risk measurement and portfolio optimization by combining distributional models with risk or performance measures into one framework. Throughout these pages, the expert authors explain the fundamentals of probability metrics, outline new approaches to portfolio optimization, and discuss a variety of essential risk measures. Using numerous examples, they illustrate a range of applications to optimal portfolio choice and risk theory, as well as applications to the area of computational finance that may be useful to financial engineers. They also clearly show how stochastic models, risk assessment, and optimization are essential to mastering risk, uncertainty, and performance measurement. Advanced Stochastic Models, Risk Assessment, and Portfolio Optimization provides quantitative portfolio managers (including hedge fund managers), financial engineers, consultants, and?academic researchers with answers to the key question of which risk measure is best for any given problem.

Svetlozar T. Rachev, PhD, Doctor of Science, is Chair-Professor at the University of Karlsruhe in the School of Economics and Business Engineering; Professor Emeritus at the University of California, Santa Barbara; and Chief-Scientist of FinAnalytica Inc.
Stoyan V. Stoyanov, PhD, is the Chief Financial Researcher at FinAnalytica Inc.
Frank J. Fabozzi, PhD, CFA, is Professor in the Practice of Finance and Becton Fellow at Yale University's School of Management and the Editor of the Journal of Portfolio Management.

Preface. Acknowledgments. About the Authors. CHAPTER 1: Concepts of Probability. 1.1 Introduction. 1.2 Basic Concepts. 1.3 Discrete Probability Distributions. 1.4 Continuous Probability Distributions. 1.5 Statistical Moments and Quantiles. 1.6 Joint Probability Distributions. 1.7 Probabilistic Inequalities. 1.8 Summary. CHAPTER 2: Optimization. 2.1 Introduction. 2.2 Unconstrained Optimization. 2.3 Constrained Optimization. 2.4 Summary. CHAPTER 3: Probability Metrics. 3.1 Introduction. 3.2 Measuring Distances: The Discrete Case. 3.3 Primary, Simple, and Compound Metrics. 3.4 Summary. 3.5 Technical Appendix. CHAPTER 4: Ideal Probability Metrics. 4.1 Introduction. 4.2 The Classical Central Limit Theorem. 4.3 The Generalized Central Limit Theorem. 4.4 Construction of Ideal Probability Metrics. 4.5 Summary. 4.6 Technical Appendix. CHAPTER 5: Choice under Uncertainty. 5.1 Introduction. 5.2 Expected Utility Theory. 5.3 Stochastic Dominance. 5.4 Probability Metrics and Stochastic Dominance. 5.5 Summary. 5.6 Technical Appendix. CHAPTER 6: Risk and Uncertainty. 6.1 Introduction. 6.2 Measures of Dispersion. 6.3 Probability Metrics and Dispersion Measures. 6.4 Measures of Risk. 6.5 Risk Measures and Dispersion Measures. 6.6 Risk Measures and Stochastic Orders. 6.7 Summary. 6.8 Technical Appendix. CHAPTER 7: Average Value-at-Risk. 7.1 Introduction. 7.2 Average Value-at-Risk. 7.3 AVaR Estimation from a Sample. 7.4 Computing Portfolio AVaR in Practice. 7.5 Backtesting of AVaR. 7.6 Spectral Risk Measures. 7.7 Risk Measures and Probability Metrics. 7.8 Summary. 7.9 Technical Appendix. CHAPTER 8: Optimal Portfolios. 8.1 Introduction. 8.2 Mean-Variance Analysis. 8.3 Mean-Risk Analysis. 8.4 Summary. 8.5 Technical Appendix. CHAPTER 9: Benchmark Tracking Problems. 9.1 Introduction. 9.2 The Tracking Error Problem. 9.3 Relation to Probability Metrics. 9.4 Examples of r.d. Metrics. 9.5 Numerical Example. 9.6 Summary. 9.7 Technical Appendix. CHAPTER 10: Performance Measures. 10.1 Introduction. 10.2 Reward-to-Risk Ratios. 10.3 Reward-to-Variability Ratios. 10.4 Summary. 10.5 Technical Appendix. Index.