带通货膨胀率及支出的双Poisson风险模型破产概率的确定

发布时间：2018-06-26 11:51

本文选题：风险模型 + 破产概率　；参考：《哈尔滨理工大学》2012年硕士论文

【摘要】：风险理论主要研究保险行业中的随机风险模型，它是金融学和精算学的基础理论，也是精算界研究的热门问题之一．作为风险理论的核心问题，破产理论是大多数学者们热衷讨论的课题．而破产理论中破产概率在风险理论中具有重要应用．一方面，破产概率可以为保险公司运营情况和保险公司的领导者提供一个危险提示；另一方面，它是判断保险公司中某一个险种能否承受金融风险的重要理论依据；更重要的是，它保证了保险公司的正常运营，，对保险监督部门的监管提供有力依据．正是由于破产概率在风险理论中的重要应用，对破产概率的研究具有重要的理论意义和实际价值．鞅论作为研究风险理论的首要方法，正逐渐成为一个非常重要的数学工具应用到各个领域中，特别是在保险行业中的应用．本文在带支出因素下的负二项风险模型的理论研究基础上，结合以往学者的研究结果，对经典风险模型进行了详尽的说明，并且考虑了通货膨胀率以及支出两方面的因素，建立新的双poisson风险模型．本文研究内容及结果主要体现在以下几个方面： 1.首先给出本文所涉及到的鞅方法与停时定理的相关理论，介绍了经典风险模型及其推广． 2.在已有的广义双poisson风险模型的基础上，考虑了通货膨胀率及支出两方面的因素，将保费的收入过程、理赔过程都考虑成poisson过程，支出过程考虑为维纳过程，从而建立新的模型．在此基础上，运用鞅方法得出模型的最终破产概率． 3.在通货膨胀率及支出两方面的因素下，考虑到保险行业的现实情况，将单险种扩展到双险种的情况，进而建立新的模型．同样运用鞅方法，得到模型的破产概率及Lundberg表达式．
[Abstract]:The risk theory mainly studies the stochastic risk model in the insurance industry, which is the basic theory of finance and actuarial science, and also one of the hot problems in the actuarial field. Bankruptcy theory is a topic that most scholars are keen to discuss. But bankruptcy probability has important application in risk theory. On the one hand, The probability of bankruptcy can provide a dangerous hint for the operation of the insurance company and the leader of the insurance company; on the other hand, it is an important theoretical basis for judging whether an insurance company can withstand financial risks; more importantly, It ensures the normal operation of the insurance company and provides a strong basis for the supervision of the insurance supervision department. It is precisely because of the important application of bankruptcy probability in the risk theory, The study of ruin probability has important theoretical significance and practical value. Martingale theory, as the first method of studying risk theory, is gradually becoming a very important mathematical tool to be applied in every field. Especially in the insurance industry. On the basis of the theoretical study of negative binomial risk model with expenditure factors and combined with the research results of previous scholars, this paper gives a detailed explanation of the classical risk model. Considering two factors of inflation and expenditure, a new double poisson risk model is established. The main contents and results of this paper are as follows: 1. Firstly, the theory of martingale method and stopping time theorem is given, and the classical risk model and its generalization are introduced. 2. On the basis of the generalized double poisson risk model, inflation rate and expenditure are taken into account. The process of premium income and claim is considered as poisson process, and the process of expenditure is considered as Wiener process. On the basis of this, the final ruin probability of the model is obtained by using martingale method. Under the two factors of inflation rate and expenditure, considering the actual situation of insurance industry, the single insurance type is extended to the double insurance type case, and a new model is established. The ruin probability and Lundberg expression of the model are also obtained by using martingale method.
【学位授予单位】：哈尔滨理工大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：F224;F840;F820.5

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