Uniform estimate on finite time ruin probabilities with random interest rate

We consider a discrete time risk model in which the net payout (insurance risk) {Xk, k = 1,2, …} are assumed to take real values and belong to the heavy-tailed class L∩D and the discount factors (financial risk) {Yk, k = 1,2, …} concentrate on [θ,L], where 0 < θ < 1, L < ∞, {Xk, k = 1,2, …}, and {Yk, k = 1,2, …} are assumed to be mutually independent. We investigate the asymptotic behavior of the ruin probability within a finite time horizon as the initial capital tends to infinity, and figure out that the convergence holds uniformly for all n ≥ 1, which is different from Tang Q H and Tsitsiashvili G (Adv Appl Prob, 2004, 36: 1278–1299).