This paper investigates the ruin probability of a renewal risk model with constant interest rate and by-claim parts. We assume that the claim size and the inter-arrival time satisfy a certain dependent structure with some additional assumptions on their distribution functions. In particular, we study the asymptotic behavior of P(R*δ (t, x) >x), which holds uniformly in a finite interval. In this way, we significantly extend the Li's result regarding the pairwise strong quasi-asymptotically independent random variables.
Wang, Lei, "Asymptotic Behavior of Finite-Time Ruin Probability in a By-Claim Risk Model with Constant Interest Rate" (2014). Student Publications. 1.