不确定风险模型的不确定生存率的研究
发布时间：2019-04-25 18:46
【摘要】：面对一个问题若碰到信息不精准或缺失的情况,此时决策常常伴随着风险.由于不确定风险的客观存可能导致潜在损失的发生,为了弥补损失,保险行业应运而生.本文借助不确定理论这门新型的数学工具,用不确定刻画风险.本文第一部分介绍了不确定理论的定义,四个基本公理,不确定测度,不确定变量和不确定变量的分布的定义.具体给出了不确定变量的运算法则.利用不确定过程及其独立增量过程给出了极值定理.本文第二部分利用不确定更新过程和不确定索赔更新过程,给出了不确定风险模型的定义,定义了不确定风险模型的生存率.利用盖伯的数学风险论导引中的最大损失总额的定义和不确定分布函数的定义以及不确定理论的极值定理求出不确定风险模型的生存率函数.本文第三部分引入传统的风险模型中带折现率的离散时间破产模型到不确定理论中,本文利用不确定生存率的定义及定理,求出了带折现率的不确定风险模型的生存率.姚凯应用不确定分布的逆分布求出更改不确定风险模型的破产率,本文在这个更改的不确定风险模型下求出不确定生存率及其生存率函数.并进行了数据模拟.
[Abstract]:In the face of a problem where information is inaccurate or missing, decision-making is often accompanied by risk. Because the objective existence of uncertain risk may lead to the occurrence of potential loss, in order to make up for the loss, insurance industry emerges as the times require. In this paper, the uncertainty theory, a new mathematical tool, is used to describe the risk. The first part of this paper introduces the definition of uncertainty theory, four basic axioms, the definition of uncertainty measure, the definition of uncertain variable and the distribution of uncertain variable. The algorithm of uncertain variables is given in detail. The extreme value theorem is given by using the uncertain process and its independent incremental process. In the second part of this paper, the definition of the uncertain risk model and the survival rate of the uncertain risk model are given by using the uncertain renewal process and the uncertain claim renewal process. The survival rate function of uncertain risk model is obtained by using the definition of maximum total loss and the definition of uncertain distribution function and the extremum theorem of uncertainty theory in the guidance of mathematical risk theory. In the third part of this paper, the discrete-time ruin model with discount rate in the traditional risk model is introduced into the uncertainty theory. By using the definition and theorem of the uncertain survival rate, the survival rate of the uncertain risk model with discount rate is obtained. Yao Kai uses the inverse distribution of the uncertain distribution to calculate the failure rate of the modified uncertain risk model. In this paper, the uncertain survival rate and the survival rate function are obtained under this modified uncertain risk model. Data simulation is carried out.
【学位授予单位】：新疆大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O211.67
本文编号：2465368
[Abstract]:In the face of a problem where information is inaccurate or missing, decision-making is often accompanied by risk. Because the objective existence of uncertain risk may lead to the occurrence of potential loss, in order to make up for the loss, insurance industry emerges as the times require. In this paper, the uncertainty theory, a new mathematical tool, is used to describe the risk. The first part of this paper introduces the definition of uncertainty theory, four basic axioms, the definition of uncertainty measure, the definition of uncertain variable and the distribution of uncertain variable. The algorithm of uncertain variables is given in detail. The extreme value theorem is given by using the uncertain process and its independent incremental process. In the second part of this paper, the definition of the uncertain risk model and the survival rate of the uncertain risk model are given by using the uncertain renewal process and the uncertain claim renewal process. The survival rate function of uncertain risk model is obtained by using the definition of maximum total loss and the definition of uncertain distribution function and the extremum theorem of uncertainty theory in the guidance of mathematical risk theory. In the third part of this paper, the discrete-time ruin model with discount rate in the traditional risk model is introduced into the uncertainty theory. By using the definition and theorem of the uncertain survival rate, the survival rate of the uncertain risk model with discount rate is obtained. Yao Kai uses the inverse distribution of the uncertain distribution to calculate the failure rate of the modified uncertain risk model. In this paper, the uncertain survival rate and the survival rate function are obtained under this modified uncertain risk model. Data simulation is carried out.
【学位授予单位】：新疆大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O211.67
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