Uniform asymptotics for the ruin probabilities of a two-dimensional renewal risk model with dependent claims and risky investments

Consider a two-dimensional renewal risk model, in which the independent and identically distributed claim-size random vectors follow a common bivariate Farlie-Gumbel-Morgenstern distribution. Assuming that the surplus is invested in a portfolio whose return follows a Lévy process and that the claim-size distribution is heavy-tailed, uniformly asymptotic estimates for two kinds of finite-time ruin probabilities of the two-dimensional risk model are obtained.