Gerber-Shiu discounted penalty function in a Sparre Andersen model with multi-layer dividend strategy

被引：27
|
作者：
Yang, Hu [1 ]
Zhang, Zhimin [1 ]
机构：
[1] Chongqing Univ, Dept Stat & Actuarial Sci, Chongqing 400030, Peoples R China
来源：
INSURANCE MATHEMATICS & ECONOMICS | 2008年 / 42卷 / 03期
关键词：
multi-layer dividend strategy; integro-differential equation; Gerber-Shiu discounted penalty function; time to ruin;
D O I：
10.1016/j.insmatheco.2007.11.004
中图分类号：
F [经济];
学科分类号：
02 ;
摘要：
This paper studies a Sparre Andersen model in which the inter-claim times are generalized Erlang(n) distributed. We assume that the premium rate is a step function depending on the current surplus level. A piecewise integro-differential equation for the Gerber-Shiu discounted penalty function is derived and solved. Finally, to illustrate the solution procedure, explicit expression for the Laplace transform of the time to ruin is given when the inter-claim times are generalized Erlang(2) distributed and the claim amounts are exponentially distributed. (c) 2007 Elsevier B.V. All rights reserved.
引用
收藏
页码：984 / 991
页数：8
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