The discounted penalty function with multi-layer dividend strategy in the phase-type risk model

被引：11

作者：

Jiang, Wuyuan ^{[1
,2
]}

Yang, Zhaojun ^{[1
]}

Li, Xinping ^{[2
]}

机构：

[1] Hunan Univ, Sch Finance & Stat, Changsha 410079, Peoples R China

[2] Hunan Inst Sci & Technol, Dept Math, Yueyang 414006, Peoples R China

来源：

STATISTICS & PROBABILITY LETTERS | 2012年 / 82卷 / 07期

基金：

国家教育部博士点专项基金资助;

关键词：

Gerber-Shiu discounted penalty function; Multi-layer dividend strategy; Integro-differential equation; Phase-type distribution;

D O I：

10.1016/j.spl.2012.03.012

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

This paper considers a Sparre Andersen model in which the inter-claim times have a phase-type distribution and the premium rate is a step function depending on the current surplus level. We derive the system of piecewise integro-differential equations for the Gerber-Shiu discounted penalty functions and obtain the closed form expressions of the Gerber-Shiu functions if the claim amount distribution belongs to the rational family. We provide a recursive approach to calculate Gerber-Shiu functions and present an example. (C) 2012 Elsevier B.V. All rights reserved.

引用

页码：1358 / 1366

页数：9

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