Tail asymptotics of generalized deflated risks with insurance applications

Let X and S is an element of (0, 1) be two independent risk variables. This paper investigates approximations of generalized deflated risks E{(XII)-I-kappa{SX > x}} with a flexible constant kappa >= 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. (C) 2016 Elsevier B.V. All rights reserved.