带有互助保险的二元相关风险模型研究

发布时间：2018-05-13 10:28

本文选题：生存概率 + 互助保险　；参考：《安徽工程大学》2017年硕士论文

【摘要】：风险是现代金融的一个本质特征,其中保险公司的生存概率是金融风险理论研究的重要内容。从风险管理的角度看,保险公司不能离开金融市场或其他保险和再保险公司而孤立的运作。保险公司和投保人为了在一定风险下获得最大收益或为保证一定收益下风险最小必然要对风险和收益进行选择,相对来说,互助保险具有一定的优势。比如船舶碰撞、石油污染、飓风和地震等灾难性事件造成大规模的损失(索赔)的发生,不同的保险公司之间通过互助保险,将一些风险和利润转移到另一家保险公司,使其避免破产。研究风险理论的过程中提出了各种各样的风险模型,盈余过程是风险理论研究的核心,因此在互助保险的条件下研究两个公司的盈余问题,即研究模型的破产概率(生存概率)等一系列问题具有一定的理论价值和现实意义。本文首先给出了有关风险模型的一些理论知识;然后在二元Cramer-Lundberg风险过程下,且两个保险公司之间拥有互相弥补亏损协议的基础上,首先,考虑两个保险公司索赔到达率均服从非齐次Poisson过程时,用鞅方法得到一元风险过程有限时间破产概率的一个上界并结合二元生存概率Laplace变换的核方程,得到二元Cramer-Lundberg风险过程下两个保险公司生存概率的一个下界,及两个保险公司险种的个体索赔额均服从指数分布时生存概率的下界估计;其次,考虑复合Poisson过程和复合二项分布两个模型分别关于两个保险公司同时生存时索赔额之间基于Copula的相关关系,对索赔到达率服从齐次复合Poisson过程的二元Cramer-Lundberg风险模型给出两个保险公司的联合生存概率的积分一微分方程及在二项分布下给出了两个保险公司的联合生存概率的递推公式。最后,研究了两个保险公司具有不确定性收入或支出情况下的破产概率,给出相应破产概率所满足的显示表达式。最后,对本文的研究结果作出了相应的总结,给出了本文的展望。
[Abstract]:Risk is an essential feature of modern finance, in which the survival probability of insurance company is an important part of financial risk theory. From a risk management perspective, insurance companies cannot operate in isolation from financial markets or other insurance and reinsurance companies. The insurance company and the policy holder must choose the risk and the income in order to obtain the maximum benefit under certain risk or to guarantee the risk minimum under the certain income, comparatively speaking, the mutual insurance has certain superiority. Catastrophic events such as ship collisions, oil pollution, hurricanes and earthquakes caused massive losses (claims), and different insurance companies transferred some risks and profits to another insurance company through mutual insurance. To avoid bankruptcy. In the course of studying risk theory, various risk models are put forward. Earnings process is the core of risk theory research, so the earnings problem of two companies is studied under the condition of mutual insurance. In other words, the study of ruin probability (survival probability) of the model has certain theoretical value and practical significance. In this paper, we first give some theoretical knowledge about risk model, then in the process of binary Cramer-Lundberg risk, and the two insurance companies have a mutual loss compensation agreement, first, When the claim arrival rates of two insurance companies are satisfied with the inhomogeneous Poisson process, an upper bound of the finite time ruin probability of the one-variable risk process is obtained by using the martingale method and the kernel equation of the Laplace transformation of the binary survival probability is obtained. We obtain a lower bound of the survival probability of two insurance companies in the process of binary Cramer-Lundberg risk, and an estimate of the survival probability of the two insurance companies from the exponential distribution. Considering the two models of compound Poisson process and compound binomial distribution, respectively, the correlation based on Copula between the claims of two insurance companies is considered. In this paper, the integro-differential equation of the joint survival probability of two insurance companies and the recurrence formula of the joint survival probability of two insurance companies are given under the binomial distribution for the binary Cramer-Lundberg risk model of the claim arrival rate from homogeneous composite Poisson process. Finally, the ruin probability of two insurance companies with uncertain income or expenditure is studied, and the expression of the corresponding ruin probability is given. Finally, the research results of this paper are summarized, and the prospect of this paper is given.
【学位授予单位】：安徽工程大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O211.67

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