Computing Sensitivities for Distortion Risk Measures

Abstract

Distortion risk measure, defined by an integral of a distorted tail probability, has been widely used in behavioral economics and risk management as an alternative to expected utility. The sensitivity of the distortion risk measure is a functional of certain distribution sensitivities. We propose a new sensitivity estimator for the distortion risk measure that uses generalized likelihood ratio estimators for distribution sensitivities as input and establish a central limit theorem for the new estimator. The proposed estimator can handle discontinuous sample paths and distortion functions.