Asymptotic ruin probabilities for a bivariate Lévy-driven risk model with heavy-tailed claims and risky investments

Abstract

Consider a general bivariate Lévy-driven risk model. The surplus process Y, starting with Y₀=x > 0, evolves according to dY_t= Y_t- dR_t -dP_t for t > 0, where P and R are two independent Lévy processes respectively representing a loss process in a world without economic factors and a process describing the return on investments in real terms. Motivated by a conjecture of Paulsen, we study the finite-time and infinite-time ruin probabilities for the case in which the loss process P has a Lévy measure of extended regular variation and the stochastic exponential of R fulfills a moment condition. We obtain a simple and unified asymptotic formula as x→∞, which confirms Paulsen's conjecture.