若干个双险种风险模型破产问题的研究

发布时间：2018-02-14 04:15

本文关键词： 分红策略双险种破产概率 Erlang(2)过程相依索赔　出处：《广西大学》2017年硕士论文　论文类型：学位论文

【摘要】：随着社会经济的快速发展加剧了保险市场的竞争,单一性质的险种已经不能满足社会的需求,因此建立多险种的风险模型来描述保险公司的经营情况已经成为现在学者们研究的热点之一.因此本文主要致力于对双险种风险模型作进一步的推广,建立相应的风险模型.主要内容为如下:1、首先研究了一类带有随机分红策略下的复合二项双险种风险模型,其两种索赔都是服从复合二项分布,当公司盈余达到或超过红利边界时,以概率q0支付一单位的红利.得到了该模型期望折现罚金函数的递推公式及其渐进估计解,最后作为应用我们还得到了破产概率、破产赤字分布函数和破产前盈余概率函数的递推公式和渐近解.2、其次考虑稀疏、随机干扰、利率等因素,建立一类双险种模型,其两类索赔分别服从泊松分布和负二项分布,利用鞅论知识导出了该模型破产概率的表达式和Lundberg不等式.3、最后讨论一类索赔相依的双险种模型,其索赔分别服从Poisson分布和Erlang(2)分布,推导出了该模型的破产概率、破产前盈余的概率函数、破产时刻赤字的分布函数及其联合分布函数所满足的积分方程,最后求出了其生存概率满足的线性微分方程,并给出具体实例.
[Abstract]:With the rapid development of social economy, the competition of insurance market has been intensified, and the single type of insurance can no longer meet the needs of the society. Therefore, it has become one of the hot topics for scholars to establish a risk model of multiple types of insurance to describe the operation of insurance companies. Therefore, this paper is mainly devoted to the further promotion of the risk model of double insurance. A corresponding risk model is established. The main contents are as follows: 1. Firstly, a kind of compound binomial insurance risk model with random dividend strategy is studied. The two claims are subordinate binomial distribution. When the earnings of the company reach or exceed the dividend boundary, a unit dividend is paid with probability Q0. The recursive formula of the expected discounted penalty function of the model and its asymptotic estimation solution are obtained. Finally, as an application, we also obtain the ruin probability. The recursive formula and asymptotic solution of the ruin deficit distribution function and the surplus probability function before bankruptcy. Secondly, considering the factors such as sparsity, random disturbance and interest rate, a kind of double insurance model is established, in which the two kinds of claims are followed by Poisson distribution and negative binomial distribution, respectively. By using martingale theory, the expression of ruin probability and Lundberg inequality. 3 are derived. Finally, a class of double insurance models with dependent claims are discussed. The ruin probability of the model is derived from Poisson distribution and Erlang2 distribution, respectively. The probability function of surplus before ruin, the distribution function of letterhead and the integral equation satisfied by its joint distribution function are obtained. Finally, the linear differential equation of its survival probability is obtained, and a concrete example is given.
【学位授予单位】：广西大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：F224;F840

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