On joint ruin probability for a bidimensional Levy-driven risk model with stochastic returns and heavy-tailed claims

In this paper we study the joint ruin problem for two insurance companies that divide between them the losses in positive proportions delta(1) and delta(2) (modeling an insurance and a re-insurance company). Assume that the surplus process of i-th (i = 1, 2) company U-i has the form of dU(i)(t) = U-i(t-)dR(i)(t) - delta(i)dP(t), t > 0, with U-i(0) = x(i) > 0, and P and R-i two Levy processes representing, respectively, a loss process and a stochastic return process. Supposing that the loss process P has a Levy measure of consistent variation and the Laplace exponent of R-i (i = 1,2) satisfies some conditions, an asymptotic estimate for this joint ruin problem is established. (C) 2016 Elsevier Inc. All rights reserved.