随机利率下的寿险精算分析

发布时间：2018-03-10 23:21

本文选题：随机利率　切入点：生存年金　出处：《山东财经大学》2014年硕士论文　论文类型：学位论文

【摘要】：在精算理论的传统研究中，，假定利率都是固定的，但是实际上利率具有一定的随机性，它会随着相关政策的变化和经济环境的改变而发生变动。在日益波动的金融市场环境和日益竞争激烈的寿险市场环境下，利率风险的度量、预测与管理变得越来越重要，因此随机利率下的寿险精算研究，也逐渐成为了研究者和实务工作者关注的焦点之一。本论文在总结概括己有研究成果的基础上,分别采用反射布朗运动与泊松过程结合、反射布朗运动与负二项分布结合两种利息力累积函数描述利率的随机性，进一步研究了常见的单生命和二元生命状态下的连续型寿险精算模型。关于单生命寿险模型，我们研究了两种利息力累积函数模型下单生命寿险保单的精算现值、年缴纯保费、均衡纯保费责任准备金、变额寿险和生存年金精算现值，得到了连续型寿险模型下它们的一般显性表达；并以反射布朗运动与泊松过程结合的利息力累积函数模型下定期寿险和生存年金模型的结果为例，通过数据模拟分析探讨了随机利率模型中的参数对精算现值的影响。关于二元生命状态寿险模型，我们基于两种利息力累积函数模型，考虑到个体之间相互独立和存在Frank copula相依的的两种情况，分别研究了二元联合生存状态和二元最后生存者状态下的寿险和生存年金的精算现值。
[Abstract]:In the traditional study of actuarial theory, it is assumed that the interest rate is fixed, but in fact the interest rate has a certain randomness. In the increasingly volatile financial market environment and the increasingly competitive life insurance market environment, the measurement, prediction and management of interest rate risk become more and more important. Therefore, the actuarial research of life insurance under random interest rate has gradually become one of the focus of researchers and practitioners. On the basis of summing up the existing research results, this paper describes the randomness of interest rate by combining the reflected Brownian motion with the Poisson process, the reflected Brownian motion with the negative binomial distribution and the cumulative function of interest force. In this paper, we further study the common actuarial models of continuous life insurance under the condition of single life and binary life. For the single life insurance model, we study the actuarial present value of life insurance policies for orders issued by two kinds of cumulative function models of interest force, and pay the annual net premium. The equilibrium pure premium liability reserve, the actuarial present value of variable life insurance and survival annuity, and the general explicit expression of them under the continuous life insurance model are obtained. The results of periodic life insurance and survival annuity model under the cumulative function model of interest force combined with reflected Brownian motion and Poisson process are taken as an example. The influence of the parameters in the stochastic interest rate model on the actuarial present value is discussed through the data simulation analysis. For the binary life state life insurance model, we base on two kinds of interest force accumulation function model. The actuarial present value of life insurance and survival annuity under the condition of binary joint survival and binary last survivor is studied, considering the two conditions of individual independence and the existence of Frank copula.
【学位授予单位】：山东财经大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：F840.62;F224

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