具有红利边界的Erlang(2)风险模型

高珊1,2

(1.中南大学数学科学与计算技术学院,湖南长沙 410075; 2.阜阳师范学院数学与计算科学学院,安徽阜阳 236041)

具有红利边界的Erlang(2)风险模型

高珊1,2

(1.中南大学数学科学与计算技术学院,湖南长沙 410075; 2.阜阳师范学院数学与计算科学学院,安徽阜阳 236041)

给出了具有边界红利策略的Erlang(2)风险模型,在此红利策略下，若保险公司的盈余在红利线以下时不支付红利,否则红利以低于保费率的常速率予以支付.对于该模型，本文推导了Gerber-Shiu折现惩罚函数所满足的两个积分-微分方程和更新方程．

Erlang(2)风险过程；折现惩罚函数；积分-微分方程；红利策略

1 引言

边界策略最初是De Finetti(1957)对二项模型提出的,最近关于复合Poisson风险模型更一般的边界策略得到广泛的研究[1-7].本文考虑具有如下边界红利策略的Erlang(2)风险模型:

δ≥0可以代表利息强度,I(…)表示示性函数,w(x1,x2)是关于x1≥0和x2＞0的非负有界函数.

2 关于mb(u)的积分-微分方程

在这部分我们将推导关于mb(u)的两个积分-微分方程,一个是当初始盈余低于边界的时候,另一个是初始盈余高于边界.令

3 关于m2(u)的更新方程

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The Erlang(2)risk model with adividend barrier

GAO Shan1,2

(1.School of Mathem atics,Central South University,Changsha 410075,China; 2.Department of Mathematics,Fuyang Normal College,Fuyang 236041,China)

In this paper,we present the Erlang(2)risk model with a dividend barrier strategy.Under such strategy,no dividends are paid if the insurer’s surp lus is below certain barrier level,when the surp lus is above this barrier level,dividends are paid at a constant rate that does not exceed the prem ium rate.For the risk model,two integro-differentialequations and a renewalequation for the Gerber-Shiu discounted penalty function are derived.

Erlang(2)risk model,discounted penalty function,integro-differential equation,dividend strategy 2000M SC:60K 20,91B30

O211.67

A

1008-5513(2009)02-0251-07

2007-09-04.

安徽省高等学校省级自然科学研究项目(KJ2007B 183).

高珊(1975-),博士,讲师,研究方向:随机过程,排队论.