On the expected discounted penalty functions for two classes of risk processes

被引：51
|
作者：
Li, SM [1 ]
Lu, Y
机构：
[1] Univ Melbourne, Dept Econ, Ctr Actuarial Studies, Parkville, Vic 3052, Australia
[2] Concordia Univ, Dept Math & Stat, Montreal, PQ, Canada
来源：
INSURANCE MATHEMATICS & ECONOMICS | 2005年 / 36卷 / 02期
基金：
加拿大自然科学与工程研究理事会;
关键词：
compound Poisson process; generalized Erlang risk process; penalty functions; integro-differential equations; martingale; generalized Lundberg's fundamental equation; Wiener process;
D O I：
10.1016/j.insmatheco.2004.12.002
中图分类号：
F [经济];
学科分类号：
02 ;
摘要：
In this paper, we consider the expected discounted penalty (Gerber-Shiu) functions for a risk model involving two independent classes of insurance risks. We assume that the two claim number processes are independent Poisson and generalized Erlang(2) processes, respectively. Laplace transforms of two types of the Gerber-Shiu functions at ruin are derived from an integro-differential equations system. Explicit results are derived when the claims from both classes are exponentially distributed. Finally, asymptotic results are obtained when the compound Poisson process converges weakly to a Wiener process. Numerical illustrations are also given. (c) 2004 Published by Elsevier B.V.
引用
收藏
页码：179 / 193
页数：15
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