Ruin time and aggregate claim amount up to ruin time for the perturbed risk process

被引：3

作者：

Rabehasaina, Landy ^{[1
]}

Tsai, Cary Chi-Liang ^{[2
]}

机构：

[1] Univ Franche Comte, Lab Math, F-25030 Besancon, France

[2] Simon Fraser Univ, Dept Stat & Actuarial Sci, Burnaby, BC V5A 1S6, Canada

来源：

SCANDINAVIAN ACTUARIAL JOURNAL | 2013年 / 03期

关键词：

Sparre-Andersen risk process; Laplace transform; Brownian motion; Markov modulated; first time passage process; risk theory;

D O I：

10.1080/03461238.2011.592262

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider the classical Sparre-Andersen risk process perturbed by a Wiener process, and study the joint distribution of the ruin time and the aggregate claim amounts until ruin by determining its Laplace transform. This is first done when the claim amounts follow respectively an exponential/Phase-type distribution, in which case we also compute the distribution of recovery time and study the case of a barrier dividend. Then the general distribution is considered when ruin occurs by oscillation, in which case a renewal equation is derived.

引用

页码：186 / 212

页数：27

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