带干扰非齐次泊松风险模型的破产概率
Ruin probability of the inhomogeneous poisson risk model
风险理论作为保险精算数学的一部分，主要是以保险公司的风险业务为主要研究对象。在风险理论的研究当中,研究者主要是通过建立接近保险公司实际运作的随机风险模型来描述保险公司的经营情况，以此为基础来探究用于实际应用的计算破产概率的方法,但是在以往的研究当中，研究者考虑的模型总是存在着一定局限性。本文从经典风险模型出发，假定保费收入的到达次数服从非齐次泊松过程，且存在着两种理赔，而且还考虑了随机扰动对保险公司经营状况的影响，建立了一类带干扰的非齐次泊松风险模型。对此模型进行研究，主要是通过鞅的方法，得到了破产概率上界满足的一般公式。
Risk theory is one of the most important parts in the actuarial mathematics. It mainly deals with the insurance operation. In the study of risk theory, the researchers mainly establish series of stochastic risk models to describe the management of the insurance company and try their best to find the method of computing the ruin probability which can be applied to the company. But in the past research, there are some localizations in their risk models. In this paper, we develop and investigate an inhomogeneous poisson risk model perturbed by a Brownian motion, the income of premium in this model is a stochastic process and there exist two kinds of claims in this model. From the discussion for this new risk model，we obtain a general formulae of upper bound for the ruin probability by martingale approach．
刘俊峰、张楠
数学
破产概率风险模型随机保费鞅
Ruin probabilityrisk modelstochastic premiummartingale
刘俊峰,张楠.带干扰非齐次泊松风险模型的破产概率[EB/OL].(2009-02-17)[2025-08-02].http://www.paper.edu.cn/releasepaper/content/200902-806.点此复制
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