Tail asymptotics of generalized deflated risks with insurance applications

Let X and S∈(0,1) be two independent risk variables. This paper investigates approximations of generalized deflated risks E{XκI{SX>x}} with a flexible constant κ≥0 under extreme value theory framework. Our findings are illustrated by three applications concerning higher-order tail approximations of deflated risks as well as approximations of the Haezendonck-Goovaerts and expectile risk measures. Numerical analyses show that higher-order approximations obtained in this paper significantly improve lower-order approximations.