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

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 Xi, and the positive stochastic discount factor over the same time period is the financial risk, denoted by Yi. Assume that {(X, Y), (Xi, Yi), 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.