摘要
考虑一类理赔间隔服从Erlang(2)分布,即Gamma(2)分布的精算风险模型.与理赔间隔服从指数分布的古典风险模型相比较,这种精算模型更易于模拟风险.首先,本文证明了生存概率R(u)满足一个积分-微分方程,然后,得到了生存概率R(u)所满足的一个指数型积分方程.最后,得到了关于生存概率R(u)的一个显示解.本文的工作可视为Dickson[1]和Dickson&Hipp[2,4]相应工作的继续和补充.
In this paper, the authors consider a class of actuarial risk models when the waiting times have an Erlang(2) distribution, the distribution same as Gamma(2). This generalizes the classical model, where the waiting times are exponential, and gives more flexibility in the modelling of a risk business. Firstly, the authors prove that the survival probability R(u) fulfils an integro-differential equation. Then an exponential-type integral equation satisfied by survival probability R(u) is obtained. Finally, an explicit solution for the survival probability R(u) is obtained in a closed form. This work is the continuation and supplement of the important corresponding work of Dickson(1998) and Dickson & Hipp(1998, 2001).
出处
《数学年刊（A辑）》
CSCD
北大核心
2005年第1期93-98,共6页
Chinese Annals of Mathematics
基金
国家社会科学基金(No.03BTJ006)国家自然科学基金(No.70271001)上海市科委基础研究重点(No.02DJ14063)资助的项目.
关键词
Erlang(2
β)分布
破产概率
生存概率
积分-微分方程
积分方程
Erlang(2, β) distribution, Ruin probability, Survival probability, Integro-Differential equation, Integral equation
