相依减因下的寿险模型研究

发布时间：2018-03-06 04:05

本文选题：衰减模型　切入点：精算现值　出处：《广州大学》2013年硕士论文　论文类型：学位论文

【摘要】：在传统的寿险模型中，被保险人是否仍在保险范围内，由其剩余寿命唯一决定，即在保险合同期内，被保险人只可能因为死亡风险而退出保险，而不考虑其他中途退出保险的可能。但在实际中，除了死亡风险外，被保险人还受到很多其他风险的影响，比如，被保险人因为伤残、失业、失踪等其他原因导致无法按时缴费而造成的保险终止，被保险人还可能因为其他原因主动退保也导致保单终止等。因此，研究多元衰减原因下的寿险模型更具有实用意义。然而，在传统的寿险精算教科书中对多减因模型均假定各个衰减原因是相互独立的，因为这样处理便于模型的推导和有关衰减概率的计算。但在实际生活中，各衰减变量之间常存在相依性，例如，个体如果发生死亡就不可能发生伤残，个体如果发生伤残有可能加速死亡等。本论文主要研究了单个个体在相依衰减原因作用下的衰减模型，以及在这个衰减模型下的精算现值等问题。还进一步研究了双重生命在相依衰减原因下的衰减模型，以及在这个衰减模型下的精算现值。本论文结构如下：第一章介绍本论文的选题背景和意义，以及国内外研究现状。第二章预备知识，包括Copula函数的概念、性质和相关测度。第三章通过Copula函数建立了单生命个体在n个相依减因作用下的衰减模型，并求得此衰减模型中个体的精算现值. 第四章主要研究了双重生命个体在n个相依减因作用下的生存概率，并给出与其相应的精算现值的计算公式. 第五章总结了本论文的研究成果和意义，，并指出了今后的研究方向。
[Abstract]:In the traditional life insurance model, whether the insured is still within the scope of insurance is only decided by his residual life, that is, during the life of the insurance contract, the insured can only withdraw from the insurance because of the risk of death. But in practice, in addition to the risk of death, the insured is also affected by many other risks, such as the insured's disability and unemployment, Other reasons, such as missing, lead to the termination of insurance due to the failure to pay on time. The insured may also take the initiative to withdraw the insurance for other reasons and also lead to the termination of the policy, etc. Therefore, It is more practical to study the life insurance model with multiple attenuation causes. However, in the traditional life insurance actuarial textbooks, it is assumed that each attenuation cause is independent of each other. Because this process facilitates the derivation of the model and the calculation of the attenuation probability. But in real life, there are often dependencies among the attenuation variables, for example, if an individual dies, it is not possible to be disabled. In this paper, we mainly study the attenuation model of individual under the action of dependent attenuation. And the actuarial present value under this attenuation model. The decay model of double life under the cause of dependent attenuation and the actuarial present value under this attenuation model are also studied. The structure of this paper is as follows:. The first chapter introduces the background and significance of this paper, as well as the current research situation at home and abroad. The second chapter is a preliminary knowledge, including the concept of Copula function, properties and related measures. In chapter 3, the attenuation model of single life individuals under the action of n dependent subtractive factors is established by Copula function, and the actuarial present value of individuals in this attenuation model is obtained. Chapter 4th mainly studies the survival probability of double living individuals under the action of n dependent subtractive factors and gives the calculation formula of the corresponding actuarial present value. Chapter 5th summarizes the research results and significance of this paper, and points out the future research direction.
【学位授予单位】：广州大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F840.62;F224

【参考文献】