Closed-form Ruin Probabilities in Classical Risk Models with Gamma Claims
Constantinescu, Corina; Samorodnitsky, Gennady; Zhu, Wei
In this paper we provide three equivalent expressions for ruin probabilities in a Cram\'er-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.
CC and WZ would like to acknowledge the European Union's Seventh Framework Programme for research, technological development and demonstration, Marie Curie grant no 318984, on Risk Analysis, Ruin and Extremes - RARE. GS would like to acknowledge the ARO MURI grant W911NF-12-1-0385
ruin probability, exact form, gamma claims