Risk Measures with Wang Transforms under Flexible Skew-generalized Settings

Abstract

To provide incentive for active risk managements, tail-preserving and coherent distortion risk measures are needed in the actuarial and financial fields. The purpose of this study is to propose extended versions of Wang transform using two different forms of flexible skew-generalized distribution functions and two different forms of flexible skew-generalized t-distributions with normal kernel and Cauchy kernel. We proved that the flexible skew-generalized risk measures in Choquet integral form with normal kernel and Cauchy kernel are coherent and degree-two tail-preserving for usual bi-atomic risk distributions.