Ruin probabilities in classical risk models with gamma claims

被引：12
|
作者：
Constantinescu, Corina [1 ]
Samorodnitsky, Gennady [2 ]
Zhu, Wei [1 ]
机构：
[1] Univ Liverpool, Inst Financial & Actuarial Math, Liverpool, Merseyside, England
[2] Cornell Univ, Sch Operat Res & Informat Engn, Ithaca, NY USA
来源：
SCANDINAVIAN ACTUARIAL JOURNAL | 2018年 / 07期
关键词：
Ruin probability; Mittag-Leffler function; gamma distribution; Laplace transform; APPROXIMATION; DEPENDENCE;
D O I：
10.1080/03461238.2017.1402817
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we provide three equivalent expressions for ruin probabilities in a Cramer-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.
引用
收藏
页码：555 / 575
页数：21
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