广义系统在保险公司盈余问题中的应用

发布时间：2018-04-05 09:17

本文选题：广义系统　切入点：状态反馈控制　出处：《东北大学》2013年硕士论文

【摘要】：本文主要研究了广义系统在保险公司盈余问题中的应用,主要内容如下：(1)介绍广义系统的发展历程和在经济中的应用,以及保险累积盈余问题的研究现状。(2)考虑保险公司累积盈余与投资收入、保费收入和理赔额的关系,以及保费收入与日常消费和理赔额的关系,又考虑了不同种保险之间的相互作用,用系统的思想建立保险公司累积盈余表达式。分析模型并给出相应系统下的计算表达式和数值例子。(3)研究保险公司盈余系统的稳定性问题。由于正常系统下的模型稳定性研究有难度,因此考虑了两种特例情况下的稳定性。当不同种保险之间没有相互作用时,系统不稳定,公司经营风险大；当不同种保险转移到同种保险的转移概率相同时,系统也不稳定。同样对广义系统下的模型进行稳定性分析,得出稳定的结论。然后针对三种不同的情形分别举出数值例子,并画出极点图给予验证。(4)分析投资回报率等不同参数对保险公司累积盈余变化的影响。由于改变参数可以带来更多的利润,但同时可能会使系统变得不稳定,因此针对不稳定的保险公司累积盈余系统,找到通过状态反馈可以使模型镇定的条件。最后考虑模型的实用价值,分析模型的因果性,正常系统下模型显然是因果的,对于广义系统下的模型利用数学归纳法证明出系统也是因果的。
[Abstract]:In this paper, we mainly study the application of singular systems in the earnings problem of insurance companies. The main contents are as follows: 1) introduce the development of singular systems and their applications in economy.Considering the relationship between the accumulated surplus of insurance companies and the investment income, the premium income and the amount of compensation, as well as the relationship between premium income and the amount of daily consumption and settlement.Considering the interaction between different kinds of insurance, the expression of accumulated earnings of insurance companies is established by systematic thinking.This paper analyzes the model and gives the computational expressions and numerical examples under the corresponding system. (3) to study the stability of the earnings system of insurance companies.Because of the difficulty of model stability in normal system, the stability of two special cases is considered.When there is no interaction between different types of insurance, the system is unstable and the company has a large operating risk; when the transfer probability of different types of insurance to the same insurance is the same, the system is also unstable.At the same time, the stability of the model under the singular system is analyzed, and the stable conclusion is obtained.Then numerical examples are given for three different cases, and the pole diagram is drawn to verify the effect of different parameters, such as return on investment, on the change of cumulative earnings of insurance companies.Since changing the parameters can bring more profit but may make the system unstable at the same time, the condition that the model can be stabilized by state feedback is found for the unstable insurance companies' cumulative earnings system.Finally, considering the practical value of the model and analyzing the causality of the model, it is obvious that the model is causality under the normal system, and the mathematical induction method is used to prove that the system is causality for the model under the generalized system.
【学位授予单位】：东北大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F842.3;TP13

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