【作者】 马素丽；

【导师】 夏亚峰；

【作者基本信息】 兰州理工大学 ， 运筹学与控制论， 2008， 硕士

【摘要】 本文对风险理论的研究与发展进行了概述,并详细综述了负二项风险模型在国内外的研究现状以及经典离散风险模型的组成部分和主要结果。在此基础上,针对目前保险业务逐渐复杂和细化的实际情况,提出了混合负二项风险模型,研究了此模型的破产参数,以期能够更真实更准确的反映保险公司的实际运营情况,便于保险公司做出统筹安排。在保险业务各种复杂的问题中,保险人依照风险的某些特征对其进行分类,但是被划入同一类中的保单仍然不可避免的存在着某种程度的非同质性。因此,对于同一类保单组合的索赔次数模型的描述,首先要确定保单组合中各个保单的索赔次数模型,然后根据同一类保单中的非同质性,确定其模型中的参数分布规律,最后再完整地描述该保单组合的索赔次数模型。这就是一种混合索赔次数模型。本文首先介绍了复合负二项风险模型的最终破产概率、有限时间内的生存概率、盈余首次和末次到达给定水平时刻的分布;接着将复合负二项风险模型中保费收取次数及其每次收取的保费都推广为随机变量,提出了混合双负二项风险模型,研究了该模型中盈余过程的数字特征、有限时间内的破产概率、最终破产概率等问题。鉴于目前保险实务中保险险种的逐渐增多,将混合双负二项风险模型进一步推广,提出了双险种的混合多负二项风险模型,研究了该模型中盈利过程的数字特征、最终破产概率、Lundberg不等式等问题。事实上,保险公司的运营过程中会时不时地出现一些随机因素,使得保险公司有些不确定的收益或者支出,为此,研究了带干扰的双险种混合多负二项风险模型的破产问题。在上述每种模型下,都得到了相应的盈余序列的性质,即盈余过程是一个平稳的独立增量过程,并得到了破产概率的具体表达形式,尤其重要的是找到了破产概率的上界,即Lundberg不等式,其较强的可操作性在保险系统的风险分析中被广泛应用,具有重要的理论和实际意义!更多还原

【Abstract】 This article has outlined the research and development of the risk theory, and summarized the negative binomial risk model in detail in the domestic and overseas present research situation as well as the constituent and the main results of the classics separate risk model. Based on this, in view of the gradually complex and specific situation on present actual insurance business, in this article I have proposed the mixed negative binomial risk model, and studied the bankrupt parameter of this model, so that the actual operation situation of insurance company can be reflected more truly and accurately, and it’s helpful for the insurance company to make the overall plan arrangement.In all kinds of complicated issues of the insurance business, the insurer carries on the classification according to the risk certain characteristics, but the chit in the same kind still is inevitable to exist some kind of degree the non-homogeneity. Therefore, regarding the claim number of times model’s description of the identical kind of chit combination, firstly must determinate the claim number of times model of each chit in the definite policy combination, then in the basis identical kind of chit’s non-homogeneity, determinate the parameter distribution rule in its model, finally describe the claim number of times model of this chit combination completely again. This is a mixed claim number of times model.This article firstly introduced the final ruin probability of the compound negative binomial risk model, the survival probability in limited time, distribution in the horizontal time of the earnings in the first time and last time; then made the insurance premium collection times and each time gathers in the negative binomial risk model be random variable, proposed the mixed double negative binomial risk model, studied the digital characteristics of the earnings process in this model, the ruin probability in the limited time, final ruin probability and so on. In view of the gradual increases of the insurance types in the present insurance practice, I promoted the mixed double negative binomial risk model further, proposed the mixed multi-negative binomial risk model of double insurance types, and studied the digital characteristics of earning process in this model, final ruin probability, Lundberg inequality and so on. In fact, in the process of the insurance company’s operation, there are some random factors once for a while, which makes insurance company have some uncertain incomes or the disbursements, so I also studied the bankrupt problems of the mixed multi-negative binomial risk model in double insurance types with disturbance items.Under the above each kind of model, all are obtained the corresponding earnings sequence nature, namely the earnings process is a steady independent increment process, which obtained the concrete expression form of ruin probability, especially more importantly had found the upper boundary of ruin probability, that is the Lundberg inequality, it is widely applied in the insurance system’s risk analysis for its strong feasibility, which has the important theoritical and the practical significance!更多还原