一类变保费且带干扰的COX风险过程的罚金折现期望函数(英文)  

On the Expected Discounted Penalty Function of a Kind of Cox Risk Process with Variable Premium Rate and Disturbed by Diffusion

作　　者：聂高琴[1] 

机构地区：[1]首都经济贸易大学统计学院,北京100070

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)

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.

关 键 词：罚金折现期望 COX过程 风险过程 函数 保费 LAPLACE变换 MARKOV过程 干扰 

分 类 号：O211.6[理学—概率论与数理统计]