A revisit to tail risk measures in the presence of bivariate regularly varying tailed insurance and financial risks

Abstract

Consider a discrete-time insurance risk model in which the one-period insurance and financial risks are assumed to be independent and identically distributed random pairs, but a strong dependence structure is allowed to exist between each pair. Recently, Q. Tang and Y. Yang employed a framework of bivariate regular variation to model the heavy tails and the dependence of the insurance and financial risks, and they also established an asymptotic formula for the finite-time ruin probability [Interplay of insurance and financial risks in a stochastic environment, Scand. Actuar. J., 2019(5):432–451, 2019]. In this paper, by adopting a different approach, we study the asymptotic behavior of some tail risk measures for the aggregate discounted net loss, including the tail probability and the conditional loss-based tail expectation. We show both analytically and numerically how the heavy tailedness and the dependence of each pair of insurance and financial risks affect the tail risk measures