摘要
本文考虑了一个风险模型的罚金折现期望函数,在此模型中,保费的收取率随索赔强度而变化,索赔到达服从COX过程,并且通过添加扩散过程来描述随机因素的影响。利用后向差分法,得到了罚金折现期望值所满足的微和分方程。当索赔强度过程为n状态的Markov过程时,通过Laplace变换,求解了该方程。
In this paper, we consider the expected discounted penalty function of a risk model with a premium rate which varies according to the intensity of claims. The occurrence of claims is described by a Cox process and the influence of stochastic factors is consieered by adding a diffusion process in the model. The integro - differential equation for the expected value of discounted penalty is derived by the backward differential argument.Further, we solve the equation when the intensity process is a homogeneons n - state Markov process by Laplace transforms.
出处
《数学理论与应用》
2009年第3期11-15,共5页
Mathematical Theory and Applications
基金
Supportey by the project of Capital University of Economics and Business (2009XJ014)
