A Probability Metrics Approach to Financial Risk MeasuresA Probability Metrics Approach to Financial Risk Measures relates the field of probability metrics and risk measures to one another and applies them to finance for the first time.

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Contents
Probability Distances and Metrics  7 
Choice under Uncertainty  40 
A Classification of Probability Distances  83 
Risk and Uncertainty  146 
Average ValueatRisk  191 
Computing AVaR through Monte Carlo  252 
Stochastic Dominance Revisited  304 
357  
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A Probability Metrics Approach to Financial Risk Measures Svetlozar T. Rachev,Stoyan V. Stoyanov,Frank J. Fabozzi No preview available  2011 
Common terms and phrases
appendix assumption asymptotic AVaR(X axioms Borel calculate chapter class of investors closedform expressions coherent risk measures common stock computed condition consider convergence corresponding cumulative prospect theory defined definition Denote density describing the return deviation measures distribution functions equal equation estimate example Fabozzi Figure finite FX(x FY(x given inequality Kantorovich metric kernel Kolmogorov metric L´evy Lévy metric limiting distribution logreturn loss minimal Monte Carlo method nonsatiable parameter payoff portfolio return preference relation primary distance probability distances probability metrics probability semidistance probability space Proof quantile quasisemidistance Rachev random variable random variables describing result return distribution riskaverse investors riskaversion function sample AVaR satisfies semimetric spectral risk measures stable distributions standard deviation stochastic dominance stochastic dominance relations stochastic order stock returns Stoyanov Student’s t distribution subset Suppose Svetlozar tail behavior tail probability Theorem tion uncertainty utility function valueatrisk