Risk Measures and Asset Pricing Models with New Versions of Wang Transform

To provide incentive for active risk managements, tail-preserving and coherent distortion risk measures are needed in the actuarial and financial fields. In this paper we propose new versions of Wang transform using two different forms of skew-normal distribution functions, and prove that the related risk measures in Choquet integral form are coherent and degree-two tail-preserving for usual bi-atomic risk distributions. Also under some plausible conditions, the portfolio optimization is explored for the capital asset pricing model where the pricing strategy uses the new Wang transforms as the distortion functions.