Consider a general bivariate Lévy-driven risk model. The surplusprocess Y, starting withY0=x > 0,evolves according todYt=Yt-dRt-dPtfor t > 0, where P and R are two independentLévy processes respectively representing a loss process in aworld without economic factors and a process describing the return oninvestments in real terms. Motivated by a conjecture of Paulsen, westudy the finite-time and infinite-time ruin probabilities for the casein which the loss process P has a Lévy measure ofextended regular variation and the stochastic exponential of Rfulfills a moment condition. We obtain a simple and unified asymptoticformula as x→∞, which confirms Paulsen'sconjecture.
"Asymptotic ruin probabilities for a bivariate Lévy-drivenrisk model with heavy-tailed claims and risky investments." J. Appl. Probab. 49 (4) 939 - 953, December 2012. https://doi.org/10.1239/jap/1354716649