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Closed-form Ruin Probabilities in Classical Risk Models with Gamma Claims

Author
Constantinescu, Corina; Samorodnitsky, Gennady; Zhu, Wei
Abstract
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.
Description
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
Date Issued
2016-12-12Subject
ruin probability, exact form, gamma claims
Type
preprint