Advanced Stochastic Models, Risk Assessment, and Portfolio Optimization -- Contents -- 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 -- BIBLIOGRAPHY -- Chapter 2 Optimization -- 2.1 INTRODUCTION -- 2.2 UNCONSTRAINED OPTIMIZATION -- 2.3 CONSTRAINED OPTIMIZATION -- 2.4 SUMMARY -- BIBLIOGRAPHY -- 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 -- BIBLIOGRAPHY -- 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 -- BIBLIOGRAPHY -- 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 -- BIBLIOGRAPHY -- 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 -- BIBLIOGRAPHY -- 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 -- BIBLIOGRAPHY -- Chapter 8 Optimal Portfolios -- 8.1 INTRODUCTION -- 8.2 MEAN-VARIANCE ANALYSIS -- 8.3 MEAN-RISK ANALYSIS -- 8.4 SUMMARY -- 8.5 TECHNICAL APPENDIX -- BIBLIOGRAPHY -- 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 -- BIBLIOGRAPHY -- 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 -- BIBLIOGRAPHY -- Index.