This paper considers a general risk model with stochastic return and a Brownian perturbation, where the claim arrival process is a general counting process and the price process of the investment portfolio is expressed as a geometric Lévy process. When the claim sizes are pairwise strong quasiasymptotically independent random variables with heavy-tailed distributions, the asymptotics of the finite-time ruin probability of this risk model have been obtained.1. Introduction. In this paper, we consider a risk model perturbed by a Brownian diffusion with stochastic return. In this risk model, the successive claim sizes, X i , i ≥ 1, form a sequence of identically distributed random variables (r.v.s) with common distribution F . The inter-arrival times, Y i , i ≥ 1, form another sequence of r.v.s. Denote the times of successive claims bywhere 1 A is the indicator function of a set A. In this risk model, the insurer is allowed to make risk free and risky investments. The price process of the investment portfolio is described as a geometric Lévy process {e R(t) , t ≥ 0}, where {R(t), t ≥

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