具有紅利邊界的Erlang(2)風(fēng)險(xiǎn)模型

高珊1,2

(1.中南大學(xué)數(shù)學(xué)科學(xué)與計(jì)算技術(shù)學(xué)院,湖南長(zhǎng)沙 410075; 2.阜陽(yáng)師范學(xué)院數(shù)學(xué)與計(jì)算科學(xué)學(xué)院,安徽阜陽(yáng) 236041)

具有紅利邊界的Erlang(2)風(fēng)險(xiǎn)模型

高珊1,2

(1.中南大學(xué)數(shù)學(xué)科學(xué)與計(jì)算技術(shù)學(xué)院,湖南長(zhǎng)沙 410075; 2.阜陽(yáng)師范學(xué)院數(shù)學(xué)與計(jì)算科學(xué)學(xué)院,安徽阜陽(yáng) 236041)

給出了具有邊界紅利策略的Erlang(2)風(fēng)險(xiǎn)模型,在此紅利策略下，若保險(xiǎn)公司的盈余在紅利線以下時(shí)不支付紅利,否則紅利以低于保費(fèi)率的常速率予以支付.對(duì)于該模型，本文推導(dǎo)了Gerber-Shiu折現(xiàn)懲罰函數(shù)所滿足的兩個(gè)積分-微分方程和更新方程．

Erlang(2)風(fēng)險(xiǎn)過(guò)程；折現(xiàn)懲罰函數(shù)；積分-微分方程；紅利策略

1 引言

邊界策略最初是De Finetti(1957)對(duì)二項(xiàng)模型提出的,最近關(guān)于復(fù)合Poisson風(fēng)險(xiǎn)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(fēng)險(xiǎn)模型:

δ≥0可以代表利息強(qiáng)度,I(…)表示示性函數(shù),w(x1,x2)是關(guān)于x1≥0和x2＞0的非負(fù)有界函數(shù).

2 關(guān)于mb(u)的積分-微分方程

在這部分我們將推導(dǎo)關(guān)于mb(u)的兩個(gè)積分-微分方程,一個(gè)是當(dāng)初始盈余低于邊界的時(shí)候,另一個(gè)是初始盈余高于邊界.令

3 關(guān)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(xué)校省級(jí)自然科學(xué)研究項(xiàng)目(KJ2007B 183).

高珊(1975-),博士,講師,研究方向:隨機(jī)過(guò)程,排隊(duì)論.