Asymptotic Properties of Generalized Shortfall Risk Measures for Heavy-tailed Risks

We study a general risk measure called the generalized shortfall risk measure, which was first introduced in Mao and Cai (2018). It is proposed under the rank-dependent expected utility framework, or equivalently induced from the cumulative prospect theory. This risk measure can be flexibly designed to capture the decision maker's behavior toward risks and wealth when measuring risk. In this paper, we derive the first- and second-order asymptotic expansions for the generalized shortfall risk mea...