{"product_id":"advanced-stochastic-models-risk-assessment-and-portfolio-optimization-the-ideal-risk-uncertainty-and-performance-measures-149-frank-j-fabozzi-series-9780470053164","title":"Advanced Stochastic Models Risk Assessment and","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis groundbreaking book extends traditional approaches of risk measurement and portfolio optimization by combining distributional models with risk or performance measures into one framework.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003ePreface xiii\u003c\/p\u003e \u003cp\u003eAcknowledgments xv\u003c\/p\u003e \u003cp\u003eAbout the Authors xvii\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 1 Concepts of Probability 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Introduction 1\u003c\/p\u003e \u003cp\u003e1.2 Basic Concepts 2\u003c\/p\u003e \u003cp\u003e1.3 Discrete Probability Distributions 2\u003c\/p\u003e \u003cp\u003e1.3.1 Bernoulli Distribution 3\u003c\/p\u003e \u003cp\u003e1.3.2 Binomial Distribution 3\u003c\/p\u003e \u003cp\u003e1.3.3 Poisson Distribution 4\u003c\/p\u003e \u003cp\u003e1.4 Continuous Probability Distributions 5\u003c\/p\u003e \u003cp\u003e1.4.1 Probability Distribution Function, Probability Density Function, and Cumulative Distribution Function 5\u003c\/p\u003e \u003cp\u003e1.4.2 The Normal Distribution 8\u003c\/p\u003e \u003cp\u003e1.4.3 Exponential Distribution 10\u003c\/p\u003e \u003cp\u003e1.4.4 Student’s t-distribution 11\u003c\/p\u003e \u003cp\u003e1.4.5 Extreme Value Distribution 12\u003c\/p\u003e \u003cp\u003e1.4.6 Generalized Extreme Value Distribution 12\u003c\/p\u003e \u003cp\u003e1.5 Statistical Moments and Quantiles 13\u003c\/p\u003e \u003cp\u003e1.5.1 Location 13\u003c\/p\u003e \u003cp\u003e1.5.2 Dispersion 13\u003c\/p\u003e \u003cp\u003e1.5.3 Asymmetry 13\u003c\/p\u003e \u003cp\u003e1.5.4 Concentration in Tails 14\u003c\/p\u003e \u003cp\u003e1.5.5 Statistical Moments 14\u003c\/p\u003e \u003cp\u003e1.5.6 Quantiles 16\u003c\/p\u003e \u003cp\u003e1.5.7 Sample Moments 16\u003c\/p\u003e \u003cp\u003e1.6 Joint Probability Distributions 17\u003c\/p\u003e \u003cp\u003e1.6.1 Conditional Probability 18\u003c\/p\u003e \u003cp\u003e1.6.2 Definition of Joint Probability Distributions 19\u003c\/p\u003e \u003cp\u003e1.6.3 Marginal Distributions 19\u003c\/p\u003e \u003cp\u003e1.6.4 Dependence of Random Variables 20\u003c\/p\u003e \u003cp\u003e1.6.5 Covariance and Correlation 20\u003c\/p\u003e \u003cp\u003e1.6.6 Multivariate Normal Distribution 21\u003c\/p\u003e \u003cp\u003e1.6.7 Elliptical Distributions 23\u003c\/p\u003e \u003cp\u003e1.6.8 Copula Functions 25\u003c\/p\u003e \u003cp\u003e1.7 Probabilistic Inequalities 30\u003c\/p\u003e \u003cp\u003e1.7.1 Chebyshev’s Inequality 30\u003c\/p\u003e \u003cp\u003e1.7.2 Fréchet-Hoeffding Inequality 31\u003c\/p\u003e \u003cp\u003e1.8 Summary 32\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 2 Optimization 35\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Introduction 35\u003c\/p\u003e \u003cp\u003e2.2 Unconstrained Optimization 36\u003c\/p\u003e \u003cp\u003e2.2.1 Minima and Maxima of a Differentiable Function 37\u003c\/p\u003e \u003cp\u003e2.2.2 Convex Functions 40\u003c\/p\u003e \u003cp\u003e2.2.3 Quasiconvex Functions 46\u003c\/p\u003e \u003cp\u003e2.3 Constrained Optimization 48\u003c\/p\u003e \u003cp\u003e2.3.1 Lagrange Multipliers 49\u003c\/p\u003e \u003cp\u003e2.3.2 Convex Programming 52\u003c\/p\u003e \u003cp\u003e2.3.3 Linear Programming 55\u003c\/p\u003e \u003cp\u003e2.3.4 Quadratic Programming 57\u003c\/p\u003e \u003cp\u003e2.4 Summary 58\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 3 Probability Metrics 61\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Introduction 61\u003c\/p\u003e \u003cp\u003e3.2 Measuring Distances: The Discrete Case 62\u003c\/p\u003e \u003cp\u003e3.2.1 Sets of Characteristics 63\u003c\/p\u003e \u003cp\u003e3.2.2 Distribution Functions 64\u003c\/p\u003e \u003cp\u003e3.2.3 Joint Distribution 68\u003c\/p\u003e \u003cp\u003e3.3 Primary, Simple, and Compound Metrics 72\u003c\/p\u003e \u003cp\u003e3.3.1 Axiomatic Construction 73\u003c\/p\u003e \u003cp\u003e3.3.2 Primary Metrics 74\u003c\/p\u003e \u003cp\u003e3.3.3 Simple Metrics 75\u003c\/p\u003e \u003cp\u003e3.3.4 Compound Metrics 84\u003c\/p\u003e \u003cp\u003e3.3.5 Minimal and Maximal Metrics 86\u003c\/p\u003e \u003cp\u003e3.4 Summary 90\u003c\/p\u003e \u003cp\u003e3.5 Technical Appendix 90\u003c\/p\u003e \u003cp\u003e3.5.1 Remarks on the Axiomatic Construction of Probability Metrics 91\u003c\/p\u003e \u003cp\u003e3.5.2 Examples of Probability Distances 94\u003c\/p\u003e \u003cp\u003e3.5.3 Minimal and Maximal Distances 99\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 4 Ideal Probability Metrics 103\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Introduction 103\u003c\/p\u003e \u003cp\u003e4.2 The Classical Central Limit Theorem 105\u003c\/p\u003e \u003cp\u003e4.2.1 The Binomial Approximation to the Normal Distribution 105\u003c\/p\u003e \u003cp\u003e4.2.2 The General Case 112\u003c\/p\u003e \u003cp\u003e4.2.3 Estimating the Distance from the Limit Distribution 118\u003c\/p\u003e \u003cp\u003e4.3 The Generalized Central Limit Theorem 120\u003c\/p\u003e \u003cp\u003e4.3.1 Stable Distributions 120\u003c\/p\u003e \u003cp\u003e4.3.2 Modeling Financial Assets with Stable Distributions 122\u003c\/p\u003e \u003cp\u003e4.4 Construction of Ideal Probability Metrics 124\u003c\/p\u003e \u003cp\u003e4.4.1 Definition 125\u003c\/p\u003e \u003cp\u003e4.4.2 Examples 126\u003c\/p\u003e \u003cp\u003e4.5 Summary 131\u003c\/p\u003e \u003cp\u003e4.6 Technical Appendix 131\u003c\/p\u003e \u003cp\u003e4.6.1 The CLT Conditions 131\u003c\/p\u003e \u003cp\u003e4.6.2 Remarks on Ideal Metrics 133\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 5 Choice under Uncertainty 139\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Introduction 139\u003c\/p\u003e \u003cp\u003e5.2 Expected Utility Theory 141\u003c\/p\u003e \u003cp\u003e5.2.1 St. Petersburg Paradox 141\u003c\/p\u003e \u003cp\u003e5.2.2 The von Neumann–Morgenstern Expected Utility Theory 143\u003c\/p\u003e \u003cp\u003e5.2.3 Types of Utility Functions 145\u003c\/p\u003e \u003cp\u003e5.3 Stochastic Dominance 147\u003c\/p\u003e \u003cp\u003e5.3.1 First-Order Stochastic Dominance 148\u003c\/p\u003e \u003cp\u003e5.3.2 Second-Order Stochastic Dominance 149\u003c\/p\u003e \u003cp\u003e5.3.3 Rothschild-Stiglitz Stochastic Dominance 150\u003c\/p\u003e \u003cp\u003e5.3.4 Third-Order Stochastic Dominance 152\u003c\/p\u003e \u003cp\u003e5.3.5 Efficient Sets and the Portfolio Choice Problem 154\u003c\/p\u003e \u003cp\u003e5.3.6 Return versus Payoff 154\u003c\/p\u003e \u003cp\u003e5.4 Probability Metrics and Stochastic Dominance 157\u003c\/p\u003e \u003cp\u003e5.5 Summary 161\u003c\/p\u003e \u003cp\u003e5.6 Technical Appendix 161\u003c\/p\u003e \u003cp\u003e5.6.1 The Axioms of Choice 161\u003c\/p\u003e \u003cp\u003e5.6.2 Stochastic Dominance Relations of Order n 163\u003c\/p\u003e \u003cp\u003e5.6.3 Return versus Payoff and Stochastic Dominance 164\u003c\/p\u003e \u003cp\u003e5.6.4 Other Stochastic Dominance Relations 166\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 6 Risk and Uncertainty 171\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Introduction 171\u003c\/p\u003e \u003cp\u003e6.2 Measures of Dispersion 174\u003c\/p\u003e \u003cp\u003e6.2.1 Standard Deviation 174\u003c\/p\u003e \u003cp\u003e6.2.2 Mean Absolute Deviation 176\u003c\/p\u003e \u003cp\u003e6.2.3 Semistandard Deviation 177\u003c\/p\u003e \u003cp\u003e6.2.4 Axiomatic Description 178\u003c\/p\u003e \u003cp\u003e6.2.5 Deviation Measures 179\u003c\/p\u003e \u003cp\u003e6.3 Probability Metrics and Dispersion Measures 180\u003c\/p\u003e \u003cp\u003e6.4 Measures of Risk 181\u003c\/p\u003e \u003cp\u003e6.4.1 Value-at-Risk 182\u003c\/p\u003e \u003cp\u003e6.4.2 Computing Portfolio VaR in Practice 186\u003c\/p\u003e \u003cp\u003e6.4.3 Backtesting of VaR 192\u003c\/p\u003e \u003cp\u003e6.4.4 Coherent Risk Measures 194\u003c\/p\u003e \u003cp\u003e6.5 Risk Measures and Dispersion Measures 198\u003c\/p\u003e \u003cp\u003e6.6 Risk Measures and Stochastic Orders 199\u003c\/p\u003e \u003cp\u003e6.7 Summary 200\u003c\/p\u003e \u003cp\u003e6.8 Technical Appendix 201\u003c\/p\u003e \u003cp\u003e6.8.1 Convex Risk Measures 201\u003c\/p\u003e \u003cp\u003e6.8.2 Probability Metrics and Deviation Measures 202\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 7 Average Value-at-Risk 207\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Introduction 207\u003c\/p\u003e \u003cp\u003e7.2 Average Value-at-Risk 208\u003c\/p\u003e \u003cp\u003e7.3 AVaR Estimation from a Sample 214\u003c\/p\u003e \u003cp\u003e7.4 Computing Portfolio AVaR in Practice 216\u003c\/p\u003e \u003cp\u003e7.4.1 The Multivariate Normal Assumption 216\u003c\/p\u003e \u003cp\u003e7.4.2 The Historical Method 217\u003c\/p\u003e \u003cp\u003e7.4.3 The Hybrid Method 217\u003c\/p\u003e \u003cp\u003e7.4.4 The Monte Carlo Method 218\u003c\/p\u003e \u003cp\u003e7.5 Backtesting of AVaR 220\u003c\/p\u003e \u003cp\u003e7.6 Spectral Risk Measures 222\u003c\/p\u003e \u003cp\u003e7.7 Risk Measures and Probability Metrics 224\u003c\/p\u003e \u003cp\u003e7.8 Summary 227\u003c\/p\u003e \u003cp\u003e7.9 Technical Appendix 227\u003c\/p\u003e \u003cp\u003e7.9.1 Characteristics of Conditional Loss Distributions 228\u003c\/p\u003e \u003cp\u003e7.9.2 Higher-Order AVaR 230\u003c\/p\u003e \u003cp\u003e7.9.3 The Minimization Formula for AVaR 232\u003c\/p\u003e \u003cp\u003e7.9.4 AVaR for Stable Distributions 235\u003c\/p\u003e \u003cp\u003e7.9.5 ETL versus AVaR 236\u003c\/p\u003e \u003cp\u003e7.9.6 Remarks on Spectral Risk Measures 241\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 8 Optimal Portfolios 245\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Introduction 245\u003c\/p\u003e \u003cp\u003e8.2 Mean-Variance Analysis 247\u003c\/p\u003e \u003cp\u003e8.2.1 Mean-Variance Optimization Problems 247\u003c\/p\u003e \u003cp\u003e8.2.2 The Mean-Variance Efficient Frontier 251\u003c\/p\u003e \u003cp\u003e8.2.3 Mean-Variance Analysis and SSD 254\u003c\/p\u003e \u003cp\u003e8.2.4 Adding a Risk-Free Asset 256\u003c\/p\u003e \u003cp\u003e8.3 Mean-Risk Analysis 258\u003c\/p\u003e \u003cp\u003e8.3.1 Mean-Risk Optimization Problems 259\u003c\/p\u003e \u003cp\u003e8.3.2 The Mean-Risk Efficient Frontier 262\u003c\/p\u003e \u003cp\u003e8.3.3 Mean-Risk Analysis and SSD 266\u003c\/p\u003e \u003cp\u003e8.3.4 Risk versus Dispersion Measures 267\u003c\/p\u003e \u003cp\u003e8.4 Summary 274\u003c\/p\u003e \u003cp\u003e8.5 Technical Appendix 274\u003c\/p\u003e \u003cp\u003e8.5.1 Types of Constraints 274\u003c\/p\u003e \u003cp\u003e8.5.2 Quadratic Approximations to Utility Functions 276\u003c\/p\u003e \u003cp\u003e8.5.3 Solving Mean-Variance Problems in Practice 278\u003c\/p\u003e \u003cp\u003e8.5.4 Solving Mean-Risk Problems in Practice 279\u003c\/p\u003e \u003cp\u003e8.5.5 Reward-Risk Analysis 281\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 9 Benchmark Tracking Problems 287\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Introduction 287\u003c\/p\u003e \u003cp\u003e9.2 The Tracking Error Problem 288\u003c\/p\u003e \u003cp\u003e9.3 Relation to Probability Metrics 292\u003c\/p\u003e \u003cp\u003e9.4 Examples of r.d. Metrics 296\u003c\/p\u003e \u003cp\u003e9.5 Numerical Example 300\u003c\/p\u003e \u003cp\u003e9.6 Summary 304\u003c\/p\u003e \u003cp\u003e9.7 Technical Appendix 304\u003c\/p\u003e \u003cp\u003e9.7.1 Deviation Measures and r.d. Metrics 305\u003c\/p\u003e \u003cp\u003e9.7.2 Remarks on the Axioms 305\u003c\/p\u003e \u003cp\u003e9.7.3 Minimal r.d. Metrics 307\u003c\/p\u003e \u003cp\u003e9.7.4 Limit Cases of \u003ci\u003eL\u003c\/i\u003e\u003csup\u003e∗\u003c\/sup\u003e\u003ci\u003e\u003csub\u003ep\u003c\/sub\u003e\u003c\/i\u003e(\u003ci\u003eX\u003c\/i\u003e, \u003ci\u003eY\u003c\/i\u003e) and Θ\u003csup\u003e∗\u003c\/sup\u003e\u003ci\u003e\u003csub\u003ep\u003c\/sub\u003e\u003c\/i\u003e(\u003ci\u003eX\u003c\/i\u003e, \u003ci\u003eY\u003c\/i\u003e) 310\u003c\/p\u003e \u003cp\u003e9.7.5 Computing r.d. Metrics in Practice 311\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 10 Performance Measures 317\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Introduction 317\u003c\/p\u003e \u003cp\u003e10.2 Reward-to-Risk Ratios 318\u003c\/p\u003e \u003cp\u003e10.2.1 RR Ratios and the Efficient Portfolios 320\u003c\/p\u003e \u003cp\u003e10.2.2 Limitations in the Application of Reward-to-Risk Ratios 324\u003c\/p\u003e \u003cp\u003e10.2.3 The STARR 325\u003c\/p\u003e \u003cp\u003e10.2.4 The Sortino Ratio 329\u003c\/p\u003e \u003cp\u003e10.2.5 The Sortino-Satchell Ratio 330\u003c\/p\u003e \u003cp\u003e10.2.6 A One-Sided Variability Ratio 331\u003c\/p\u003e \u003cp\u003e10.2.7 The Rachev Ratio 332\u003c\/p\u003e \u003cp\u003e10.3 Reward-to-Variability Ratios 333\u003c\/p\u003e \u003cp\u003e10.3.1 RV Ratios and the Efficient Portfolios 335\u003c\/p\u003e \u003cp\u003e10.3.2 The Sharpe Ratio 337\u003c\/p\u003e \u003cp\u003e10.3.3 The Capital Market Line and the Sharpe Ratio 340\u003c\/p\u003e \u003cp\u003e10.4 Summary 343\u003c\/p\u003e \u003cp\u003e10.5 Technical Appendix 343\u003c\/p\u003e \u003cp\u003e10.5.1 Extensions of STARR 343\u003c\/p\u003e \u003cp\u003e10.5.2 Quasiconcave Performance Measures 345\u003c\/p\u003e \u003cp\u003e10.5.3 The Capital Market Line and Quasiconcave Ratios 353\u003c\/p\u003e \u003cp\u003e10.5.4 Nonquasiconcave Performance Measures 356\u003c\/p\u003e \u003cp\u003e10.5.5 Probability Metrics and Performance Measures 357\u003c\/p\u003e \u003cp\u003eIndex 361\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49402273202519,"sku":"9780470053164","price":59.25,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780470053164.jpg?v=1730479910","url":"https:\/\/bookcurl.com\/products\/advanced-stochastic-models-risk-assessment-and-portfolio-optimization-the-ideal-risk-uncertainty-and-performance-measures-149-frank-j-fabozzi-series-9780470053164","provider":"Book Curl","version":"1.0","type":"link"}