Distortion risk measures under skew normal settings

Abstract

Coherent distortion risk measure is needed in the actuarial and financial fields in order to provide incentive for active risk management. The purpose of this study is to propose extended versions of Wang transform using skew normal distribution functions. The main results show that the extended version of skew normal distortion riskmeasure is coherent and its transform satisfies the classic capital asset pricing model. Properties of the stock price model under log-skewnormal and its transform are also studied. A simulation based on the skew normal transforms is given for a insurance payoff function.