具有紅利邊界的Erlang(2)風險模型

高珊1,2

(1.中南大學數學科學與計算技術學院,湖南長沙 410075; 2.阜陽師范學院數學與計算科學學院,安徽阜陽 236041)

具有紅利邊界的Erlang(2)風險模型

高珊1,2

(1.中南大學數學科學與計算技術學院,湖南長沙 410075; 2.阜陽師范學院數學與計算科學學院,安徽阜陽 236041)

給出了具有邊界紅利策略的Erlang(2)風險模型,在此紅利策略下，若保險公司的盈余在紅利線以下時不支付紅利,否則紅利以低于保費率的常速率予以支付.對于該模型，本文推導了Gerber-Shiu折現懲罰函數所滿足的兩個積分-微分方程和更新方程．

Erlang(2)風險過程；折現懲罰函數；積分-微分方程；紅利策略

1 引言

邊界策略最初是De Finetti(1957)對二項模型提出的,最近關于復合Poisson風險模型更一般的邊界策略得到廣泛的研究[1-7].本文考慮具有如下邊界紅利策略的Erlang(2)風險模型:

δ≥0可以代表利息強度,I(…)表示示性函數,w(x1,x2)是關于x1≥0和x2＞0的非負有界函數.

2 關于mb(u)的積分-微分方程

在這部分我們將推導關于mb(u)的兩個積分-微分方程,一個是當初始盈余低于邊界的時候,另一個是初始盈余高于邊界.令

3 關于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.

安徽省高等學校省級自然科學研究項目(KJ2007B 183).

高珊(1975-),博士,講師,研究方向:隨機過程,排隊論.