Asymptotics for the finite-time ruin probability in a discrete-time risk model with dependent insurance and financial risks*

Abstract

We consider a discrete-time risk model with insurance and financial risks. Within period i ≥ 1, the real-valued net insurance loss caused by claims is the insurance risk, denoted by X i , and the positive stochastic discount factor over the same time period is the financial risk, denoted by Y i . Assume that {(X, Y), (X i , Y i ), i ≥ 1} form a sequence of independent identically distributed random vectors. In this paper, we investigate a discrete-time risk model allowing a dependence structure between the two risks. When (X, Y ) follows a bivariate Sarmanov distribution and the distribution of the insurance risk belongs to the class ℒ(γ) for some γ > 0, we derive the asymptotics for the finite-time ruin probability of this discrete-time risk model.