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H. Albrecher et al., « Asymptotic results for renewal risk models with risky investments », Serveur académique Lausannois, ID : 10.1016/j.spa.2012.05.017
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We consider a renewal jump-diffusion process, more specifically a renewal 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 analytic method for investigating the asymptotic behavior of ruin probabilities and related quantities, in models with light- or heavy-tailed jumps, whenever the distribution of the time between jumps has rational Laplace transform.