| 一类变保费且带干扰的COX风险过程的罚金折现期望函数 |
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| 引用本文： | 聂高琴.一类变保费且带干扰的COX风险过程的罚金折现期望函数[J].数学理论与应用,2009(3):11-15. |
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| 作者姓名： | 聂高琴 |
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| 作者单位： | 首都经济贸易大学统计学院,北京100070 |
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| 基金项目： | Supportey by the project of Capital University of Economics and Business （2009XJ014） |
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| 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。
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| 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 |
On the Expected Discounted Penalty Function of a Kind of Cox Risk Process with Variable Premium Rate and Disturbed by Diffusion |
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| Nie Gaoqin.On the Expected Discounted Penalty Function of a Kind of Cox Risk Process with Variable Premium Rate and Disturbed by Diffusion[J].Mathematical Theory and Applications,2009(3):11-15. |
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| Authors: | Nie Gaoqin |
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| Institution: | Nie Gaoqin (School of Statistics, Capital University of Economies and Business, Beijing, 100070) |
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| Abstract: | 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. |
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| Keywords: | Expected discounted penalty Risk process Variable premium rate Markov intensity |
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