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

页码：555 / 575

页数：21

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