A Probability Metrics Approach to Financial Risk Measures
John Wiley & Sons, Mar 10, 2011 - Business & Economics - 392 pages
A 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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appendix assumption asymptotic AVaR(X axioms Borel calculate chapter class of investors closed-form 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 LÚvy metric limiting distribution log-return loss minimal Monte Carlo method non-satiable parameter payoff portfolio return preference relation primary distance probability distances probability metrics probability semidistance probability space Proof quantile quasi-semidistance Rachev random variable random variables describing result return distribution risk-averse investors risk-aversion 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 value-at-risk