Asymptotics for a discrete-time risk model with Gamma-like insurance risks

Abstract

Consider a discrete-time insurance risk model with insurance and financial risks. Within period , the net insurance loss is denoted by and the stochastic discount factor over the same time period is denoted by . Assume that form a sequence of independent and identically distributed real-valued random variables with common distribution ; are another sequence of independent and identically distributed positive random variables with common distribution ; and the two sequences are mutually independent. Under the assumptions that is Gamma-like tailed and has a finite upper endpoint, we derive some precise formulas for the tail probability of the present value of aggregate net losses and the finite-time and infinite-time ruin probabilities. As an extension, a dependent risk model is considered, where each random pair of the net loss and the discount factor follows a bivariate Sarmanov distribution.