ASYMPTOTIC RUIN PROBABILITIES IN A GENERALIZED JUMP-DIFFUSION RISK MODEL WITH CONSTANT FORCE OF INTEREST

Abstract. This paper studies the asymptotic behavior of the finite-timeruin probability in a jump-diffusion risk model with constant force of in-terest, upper tail asymptotically independent claims and a general count-ing arrival process. Particularly, if the claim inter-arrival times follow acertain dependence structure, the obtained result also covers the case ofthe infinite-time ruin probability. 1. IntroductionIn this paper, we consider the asymptotic ruin probabilities in a generalizedjump-diffusion risk model with constant force of interest, where the claim sizes{X i ,i≥ 1} are a sequence of nonnegative, but not necessarily independent,random variables (r.v.s) with distributions F i , i≥ 1, respectively, while theclaim arrival process {N(t),t≥ 0} is a general counting process, independentof {X i ,i≥ 1}. Hence, the aggregate claim amount up to time t≥ 0 isS(t) = N X (t)i=1 X i with S(t) = 0 if N(t) = 0. Assume that the total amount of premiums accu-mulated up to time t≥ 0, denoted by C(t), is a nonnegative and nondecreasingstochastic process with C(0) = 0 and C(t) <∞ almost surely (a.s.) for every0 ≤ t<∞, and that the diffusion process, as a perturbed term, {B(t),t≥ 0} isa standard Brownian motion with volatility parameter σ≥ 0 and independentof the other sources of randomness. We notice that in practice, the diffusion-perturbed term can be interpreted as an additional uncertainty of the aggregateclaims or the premium income of an insurance company. Let r≥ 0 be the con-stant force of interest and x≥ 0 be the insurer’s initial reserve. Then the total