Asymptotic results for renewal risk models with risky investments

We consider a renewal jump-diffusion process, more specifically a re-newal insurance risk model with investments in a stock whose price is modeled by a geometric Brownian motion. Using Laplace transforms and regular variation theory, we introduce a transparent and unifying an-alytic method for investigating the asymptotic behavior of ruin probabil-ities and related quantities, in models with light- or heavy-tailed jumps, whenever the distribution of the time between jumps has rational Laplace transform.