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Asymptotic results for renewal risk models with risky investments |
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| Authors: | Hansjoerg Albrecher Corina Constantinescu Enrique Thomann |
| Affiliation: | 1. Department of Actuarial Science, Faculty of Business and Economics, University of Lausanne, UNIL-Dorigny, 1015 Lausanne, Switzerland;2. Swiss Finance Institute, University of Lausanne, UNIL-Dorigny, 1015 Lausanne, Switzerland;3. Institute for Financial and Actuarial Mathematics, Department of Mathematical Sciences, University of Liverpool, L69 7ZL Liverpool, United Kingdom;4. Oregon State University, Department of Mathematics, Corvallis, OR, 97331, USA |
| Abstract: | 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. |
| Keywords: | Renewal jump&ndash diffusion process Ruin probability Sparre Andersen risk model Investment Rational Laplace transform Regular variation |
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