随机观察的复合泊松风险模型的研究

发布时间：2019-03-17 11:41

【摘要】：在社会经济不断发展的条件下,金融行业以及保险行业都得到了蓬勃的发展。风险理论目前作为决策者或者经营者对风险进行预测和评估的一般理论已经广泛地应用于金融行业和保险行业等领域之中。在保险数学中破产理论已经成为了风险理论的核心内容,它是近几十年来风险理论中研究的一个中心问题。它的研究既有概率理论上的意义又有实际的应用背景。Gerber与Shiu在文献中提出了期望折现罚金函数(后面被称为Gerber-Shiu函数),由于它具有很多的优点,于是对于期望折现罚金函数的研究一直是保险精算研究领域的一个热点问题,关于罚金函数的研究可以查看文献。本文主要是在复合Poisson风险模型的基础上,考虑随机观察时间,由连续的情况转化为连续离散结合的情况。然后通过在不同方面进行推广而得到不同的风险模型,并研究其折现罚金函数,最终得到微分-积分方程。本文主要做了以下的工作： 1.将随机观察的复合Poisson风险模型推广为带布朗运动的随机观察的复合Poisson风险模型,然后计算在该风险模型下的折现罚金函数所满足的积分-微分方程。 2.将随机观察的复合Poisson风险模型推广为带随机收入的随机观察的复合Poisson风险模型,然后计算在该风险模型下的折现罚金函数所满足的积分-微分方程。
[Abstract]:Under the condition of continuous development of social economy, the financial industry and the insurance industry have obtained the vigorous development. At present, risk theory has been widely used in financial industry and insurance industry as a general theory of risk prediction and evaluation by decision makers or operators. Bankruptcy theory has become the core content of risk theory in insurance mathematics. It is a central problem in risk theory in recent decades. Its research has both theoretical significance and practical application background. Gerber and Shiu proposed the expected discounted penalty function (later called Gerber-Shiu function) in the literature, because it has many advantages. Therefore, the research on the expected discounted penalty function has always been a hot issue in the field of actuarial insurance research, and the research on the penalty function can be viewed in the literature. In this paper, based on the compound Poisson risk model, the random observation time is taken into account, and the continuous case is transformed into the continuous discrete combination case. Then different risk models are obtained by generalizing them in different aspects, and the discounted penalty function is studied. Finally, the differential-integral equation is obtained. The main work of this paper is as follows: 1. The random observed composite Poisson risk model is extended to the stochastic observed composite Poisson risk model with Brownian motion, and then the integral-differential equations satisfied by the discounted penalty function under this risk model are calculated. 2. The random observed compound Poisson risk model is extended to the composite Poisson risk model with random income, and then the Integro-differential equations satisfied by the discounted penalty function under the risk model are calculated.
【学位授予单位】：湖南师范大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F840.3;O211.67;F224

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