Beschreibung
InhaltsangabeChapter 1 Introduction. 1.1 Probability metrics. 1.2 Applications in finance. Chapter 2 Probability distances and metrics. 2.1 Introduction. 2.2 Some examples of probability metrics. 2.3 Distance and semidistance spaces. 2.4 Definitions of probability distances and metrics. 2.5 Summary. 2.6 Technical appendix. Chapter 3 Choice under uncertainty. 3.1 Introduction. 3.2 Expected utility theory. 3.3 Stochastic dominance. 3.4 Probability metrics and stochastic dominance. 3.5 Cumulative Prospect Theory. 3.6 Summary. 3.7 Technical appendix. Chapter 4 A classification of probability distances. 4.1 Introduction. 4.2 Primary distances and primary metrics. 4.3 Simple distances and metrics. 4.4 Compound distances and moment functions. 4.5 Ideal probability metrics. 4.6 Summary. 4.7 Technical appendix. Chapter 5 Risk and uncertainty. 5.1 Introduction. 5.2 Measures of dispersion. 5.3 Probability metrics and dispersion measures. 5.4 Measures of risk. 5.5 Risk measures and dispersion measures. 5.6 Risk measures and stochastic orders. 5.7 Summary. 5.8 Technical appendix. Chapter 6 Average value-at-risk. 6.1 Introduction. 6.2 Average value-at-risk. 6.2.1 AVaR for stable distributions. 6.3 AVaR estimation from a sample. 6.4 Computing portfolio AVaR in practice. 6.5 Backtesting of AVaR. 6.6 Spectral risk measures. 6.7 Risk measures and probability metrics. 6.8 Risk measures based on distortion functionals. 6.9 Summary. 6.10 Technical appendix. Chapter 7 Computing AVaR through Monte Carlo. 7.1 Introduction. 7.2 An illustration of Monte Carlo variability. 7.3 Asymptotic distribution, classical conditions. 7.4 Rate of convergence to the normal distribution. 7.5 Asymptotic distribution, heavy-tailed returns. 7.6 Rate of convergence, heavy-tailed returns. 7.7 On the choice of a distributional model. 7.8 Summary. 7.9 Technical appendix. Chapter 8 Stochastic dominance revisited. 8.1 Introduction. 8.2 Metrization of preference relations. 8.3 The Hausdorff metric structure. 8.4 Examples. 8.5 Utilitytype representations. 8.6 Almost stochastic orders and degree of violation. 8.7 Summary. 8.8 Technical appendix.
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