阈红利策略下风险模型的相关问题的研究

发布时间：2018-07-15 15:37

【摘要】：保险公司与人们的生活息息相关,它在一定程度上保障了人们的生活,承担了各种极端事件所带给人的部分经济损失。保险公司的正常运作是受很多因素的影响,如投保人数、索赔因素等,而破产问题是衡量保险公司是否能正常运行的一个标准。风险理论则是针对现实生活中保险公司的盈余情况建立风险模型,用概率的方法研究其破产的相关问题。最初的风险理论是建立在理想的条件下,其中单位时间内保费收取为常数,索赔到达强度也为常数,随着人们对随机现象更深入的理解,研究方法的不断改进与多样化,人们越来越倾向于将风险模型不断改进,使其趋于现实化。其中主要的改进有以下三个方面：一是改变其索赔过程,推广泊松过程或就其索赔强度进行推广；二是将单位保费收取常量c改为变量,这是由于现实中保费率受一些因素影响往往是变化的；三是将扰动因素加入经典风险模型中,即将现实保险公司经营中的红利、利率等因素加入了模型。现实中保险公司的险种各不相同,不同险种的索赔到达过程各不相同,如海啸、地震发生的时间间隔分布用Sparre Andersen风险模型来描述往往好于其他模型,COx风险模型更多的应用于医疗领域,条件泊松模型可应用于酒驾事故的分析。用更符合的模型去刻画风险,使公司破产问题的研究与经营前景的估计更有利于人们掌握对风险的控制与防范。本文在众多研究成果基础上,综合考虑了索赔到达过程、红利和利率因素,就三种不同风险模型—Erlang(n)风险模型、Cox风险模型和条件泊松风险模型进行研究。由于索赔到达过程是一种随机过程,而概率主要是研究随机事件,故研究方法主要是基于概率领域的方法,如随机过程、风险理论和概率论等知识。本文首先介绍了风险理论的研究背景与意义、国内外研究现状。其次,在经典风险模型的基础上,研究其推广模型Erlang (n)风险模型,其索赔时间间隔分布不再是指数分布,并用微分法求出了在常数红利下的折现罚函数所满足的微分方程和在常利率与常数红利下的折现罚函数所满足的微分方程。对于Cox风险模型,其索赔到达强度是与时间有关的一个量,用鞅的方法研究了此模型在线性红利下的破产概率的一个界限和在常利率与线性红利下的破产概率的一个界限。最后是条件泊松风险模型,其索赔到达强度是一个变量,通过鞅的构造研究了其在线性红利下的破产概率的一个界限和在常利率与线性红利下的破产概率的一个界限。
[Abstract]:Insurance companies are closely related to people's lives. To a certain extent, insurance companies protect people's lives and bear part of the economic losses brought by various extreme events. The normal operation of insurance companies is affected by many factors, such as the number of policy holders, claim factors and so on. Risk theory is to establish a risk model for the earnings of insurance companies in real life, and use the method of probability to study the problems related to the bankruptcy of insurance companies. The initial risk theory is based on ideal conditions, in which the premium per unit time is constant, and the claim arrival intensity is constant. With the further understanding of the stochastic phenomenon, the research methods have been improved and diversified. More and more people tend to improve the risk model and make it more realistic. The main improvements are as follows: first, changing its claim process, popularizing the Poisson process or popularizing its claim intensity; second, changing the unit premium charge constant c into a variable. This is because the real insurance rate is influenced by some factors, and the third is to add the disturbance factor into the classical risk model, that is, the dividend and interest rate in the operation of the real insurance company are added to the model. In reality, insurance companies have different types of insurance, and claims for different types of insurance arrive in different processes, such as tsunamis, The time interval distribution of earthquakes is described by Sparre Andersen risk model, which is better than other models. The conditional Poisson model can be applied to the analysis of alcohol driving accidents. A more consistent model is used to depict risks, so that the study of corporate bankruptcy and the estimation of business prospects are more helpful for people to grasp the control and prevention of risks. On the basis of many research results, this paper studies three different risk models -Erlang (n) risk model and conditional Poisson risk model, considering the factors of claim arrival process, dividend and interest rate. Because the claim arrival process is a stochastic process and the probability is mainly a study of random events, the research methods are mainly based on the methods of probability domain, such as stochastic process, risk theory and probability theory. This paper first introduces the research background and significance of risk theory, domestic and foreign research status. Secondly, based on the classical risk model, the Erlang (n) risk model is studied, and the claim interval distribution is no longer exponential. The differential equation satisfied by the discount penalty function under the constant dividend and the differential equation satisfied by the discount penalty function under the constant interest rate and the constant dividend are obtained by using the differential method. For the Cox risk model, the claim arrival strength is a time-dependent quantity. The martingale method is used to study a bound of the ruin probability under the linear dividend and the ruin probability under the constant interest rate and the linear dividend. Finally, the conditional Poisson risk model, whose claim arrival strength is a variable, is studied by the construction of martingale. A limit of ruin probability under linear dividend and a limit of ruin probability under constant interest rate and linear dividend are studied.
【学位授予单位】：安徽工程大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：F224;F840.31

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