Efficient Portfolio Analysis Using Distortion Risk Measures

Distortion risk measures including the Value-at-Risk and the Tail-VaR are currently suggested by the regulators in Finance (Basel II) and Insurance (Solvency II). We introduce nonparametric estimators of the sensitivity of distortion risk measures (DRM) with respect to portfolio allocation. These estimators are used to derive the estimated efficient portfolio allocations when distortion risk measures define the constraints and the objectives, to study their asymptotic distributional properties, and to construct tests for the hypothesis of portfolio efficiency.