Advanced stochastic models, risk assessment, and portfolio optimization: the ideal risk, uncertainty, and performance measures

INDICE: Preface. Acknowledgments. About the Authors. CHAPTER 1: Concepts ofProbability. 1.1 Introduction. 1.2 Basic Concepts. 1.3 Discrete Probability Distributions. 1.3.1 Bernoulli Distribution. 1.3.2 Binomial Distribution. 1.3.3Poisson Distribution. 1.4 Continuous Probability Distributions. 1.4.1 Probability Distribution Function, Probability Density Function, and Cumulative Distribution Function. 1.4.2 The Normal Distribution. 1.4.3 Exponential Distribution. 1.4.4 Students t-distribution. 1.4.5 Extreme Value Distribution. 1.4.6 Generalized Extreme Value Distribution. 1.5 Statistical Moments and Quantiles. 1.5.1 Location. 1.5.2 Dispersion. 1.5.3 Asymmetry. 1.5.4 Concentration in Tails. 1.5.5 Statistical Moments. 1.5.6 Quantiles. 1.5.7 Sample Moments. 1.6 Joint Probability Distributions. 1.6.1 Conditional Probability. 1.6.2 Definition of Joint Probability Distributions. 1.6.3 Marginal Distributions. 1.6.4 Dependence of Random Variables. 1.6.5 Covariance and Correlation. 1.6.6 Multivariate Normal Distribution. 1.6.7 Elliptical Distributions. 1.6.8 Copula Functions. 1.7 Probabilistic Inequalities. 1.7.1 Chebyshevs Inequality. 1.7.2 Fr´echet-Hoeffding Inequality. 1.8 Summary. CHAPTER 2: Optimization. 2.1 Introduction. 2.2 Unconstrained Optimization. 2.2.1 Minima and Maxima of a Differentiable Function.2.2.2 Convex Functions. 2.2.3 Quasiconvex Functions. 2.3 Constrained Optimization. 2.3.1 Lagrange Multipliers. 2.3.2 Convex Programming. 2.3.3 Linear Programming. 2.3.4 Quadratic Programming. 2.4 Summary. CHAPTER 3: Probability Metrics. 3.1 Introduction. 3.2 Measuring Distances: The Discrete Case. 3.2.1 Sets of Characteristics. 3.2.2 Distribution Functions. 3.2.3 Joint Distribution. 3.3Primary, Simple, and Compound Metrics. 3.3.1 Axiomatic Construction. 3.3.2 Primary Metrics. 3.3.3 Simple Metrics. 3.3.4 Compound Metrics. 3.3.5 Minimal andMaximal Metrics. 3.4 Summary. 3.5 Technical Appendix. 3.5.1 Remarks on the Axiomatic Construction of Probability Metrics. 3.5.2 Examples of Probability Distances. 3.5.3 Minimal and Maximal Distances. CHAPTER 4: Ideal Probability Metrics../…CHAPTER 8: Optimal Portfolios. 8.1 Introduction. 8.2 Mean-Variance Analysis. 8.2.1 Mean-Variance Optimization Problems. 8.2.2 The Mean-Variance Efficient Frontier. 8.2.3 Mean-Variance Analysis and SSD. 8.2.4 Adding a Risk-Free Asset. 8.3 Mean-Risk Analysis. 8.3.1 Mean-Risk Optimization Problems. 8.3.2 The Mean-Risk Efficient Frontier. 8.3.3 Mean-Risk Analysis and SSD. 8.3.4 Risk versus Dispersion Measures. 8.4 Summary. 8.5 Technical Appendix. 8.5.1 Types ofConstraints. 8.5.2 Quadratic Approximations to Utility Functions. 8.5.3 Solving Mean-Variance Problems in Practice. 8.5.4 Solving Mean-Risk Problems in Practice. 8.5.5 Reward-Risk Analysis. CHAPTER 9: Benchmark Tracking Problems. 9.1Introduction. 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. 9.7.1 Deviation Measures and r.d. Metrics. 9.7.2 Remarks on the Axioms. 9.7.3 Minimal r.d. Metrics. CHAPTER 10: Performance Measures. 10.1Introduction. 10.2 Reward-to-Risk Ratios. 10.2.1 RR Ratios and the Efficient Portfolios. 10.2.2 Limitations in the Application of Reward-to-Risk Ratios. 10.2.3 The STARR. 10.2.4 The Sortino Ratio. 10.2.5 The Sortino-Satchell Ratio. 10.2.6 A One-Sided Variability Ratio. 10.2.7 The Rachev Ratio. 10.3 Reward-to-Variability Ratios. 10.3.1 RV Ratios and the Efficient Portfolios. 10.3.2 The Sharpe Ratio. 10.3.3 The Capital Market Line and the Sharpe Ratio. 10.4 Summary. 10.5 Technical Appendix. 10.5.1 Extensions of STARR. 10.5.2 Quasiconcave Performance Measures. 10.5.3 The Capital Market Line and Quasiconcave Ratios. 10.5.4 Nonquasiconcave Performance Measures. 10.5.5 Probability Metrics and Performance Measures. Index.

• ISBN: 978-0-470-05316-4
• Editorial: John Wiley & Sons
• Encuadernacion: Cartoné
• Páginas: 382
• Fecha Publicación: 02/04/2008
• Nº Volúmenes: 1
• Idioma: Inglés