Ruin probabilities in classical risk models with gamma claims |
| |
| Authors: | Corina Constantinescu Gennady Samorodnitsky |
| |
| Institution: | 1. Institute for Financial and Actuarial Mathematics, University of Liverpool, Liverpool, UK.;2. School of Operations Research and Information Engineering, Cornell University, Ithaca, NY, USA. |
| |
| Abstract: | In this paper, we provide three equivalent expressions for ruin probabilities in a Cramér–Lundberg model with gamma distributed claims. The results are solutions of integro-differential equations, derived by means of (inverse) Laplace transforms. All the three formulas have infinite series forms, two involving Mittag–Leffler functions and the third one involving moments of the claims distribution. This last result applies to any other claim size distributions that exhibits finite moments. |
| |
| Keywords: | Ruin probability Mittag–Leffler function gamma distribution Laplace transform |
|
|
