Consider a general bivariate Lévy-driven risk model. The surplus process Y, starting with Y0=x > 0, evolves according to dYt= Yt- dRt -dPt 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.
"Asymptotic ruin probabilities for a bivariate Lévy-driven risk model with heavy-tailed claims and risky investments." J. Appl. Probab. 49 (4) 939 - 953, December 2012. https://doi.org/10.1239/jap/1354716649