随机利率下的分期缴费联合寿险精算模型研究

发布时间：2018-05-10 12:16

本文选题：随机利率 + 分期付款　；参考：《哈尔滨工程大学》2014年硕士论文

【摘要】：在实际生活中,人们可能会面临疾病和意外事故所带来的死亡风险,虽然个体面临的死亡风险难以预测,但从群体角度来看,风险具有稳定性。对保险公司来说,单个投保人的死亡风险难以预测,但由于保险公司的客户并不是单一个体,而是多个群体,所以投保人越多保险公司的损失风险就越分散,因此死亡率的变化并不会引起纯保费的巨大变化。死亡率和利率是厘定寿险纯保费的两个主要因素,从历史数据来看利率具有很强的随机性,影响利率的因素很多,很难用一精确的数学方法来描绘利率的波动,传统精算学中的利率从保单生效的那一刻起固定不变,寿险保单的有效期动辄几十年,资金运作周期较长,利率的波动给保险公司带来了巨大的风险。因此厘定保费时利率比死亡率更加重要,对随机利率的研究符合社会发展的需求,越来越多的学者致力于随机利率的研究。随着当今社会人们生活成本的增加,分期付款应运而生。在购房或购车时,人们可以选择按月缴费,但以往的寿险都是按年缴纳保费。最近中国多家寿险公司相继推出了新型寿险,这种新型寿险可以按季度缴费,甚至是按月缴费。因此,本文研究随机利率下的分期缴费寿险精算模型。本文首先介绍随机过程和寿险精算模型的一些基本概念。其次,采用Wiener过程与Poisson过程模拟利率的波动,构建了随机利率下的分期缴费联合寿险精算模型,分析了通货膨胀对投保人的影响,将居民消费价格指数引入寿险精算模型中,构建了增额寿险精算模型。推导出了分期缴费形式下的趸缴纯保费、均衡纯保费、责任准备金以及保险公司损失风险。再次,分别在Gompertz假设和UDD假设条件下化简了分期缴费寿险模型,得到了趸缴纯保费、均衡纯保费、责任准备金以及保险公司损失风险的相应表达式。最后,通过数值计算分析了给付函数、分期付款的次数以及投保期限等对保费与责任准备金的影响,并根据历年的利率变化数据检验了随机利率模型。该模型不仅能减少投保人缴纳的保费,并且能够减小保险公司损失风险,该模型具有实际应用价值。
[Abstract]:In real life, people may face the risk of death caused by disease and accidents. Although the risk of death faced by individuals is difficult to predict, the risk is stable from a group point of view. For an insurance company, the risk of death of a single policyholder is difficult to predict, but because the clients of the insurance company are not a single individual, but rather more groups, the more insured the insurance company, the more the risk of loss will be dispersed. So a change in mortality does not cause a huge change in net premiums. Mortality and interest rate are the two main factors in determining the net premium of life insurance. From the historical data, interest rate is very random, and there are many factors affecting interest rate. It is difficult to describe the fluctuation of interest rate by a precise mathematical method. The interest rate in traditional actuarial science is fixed from the moment when the policy becomes effective. The life insurance policy is valid for dozens of years and the capital operation period is longer. The fluctuation of interest rate brings huge risks to the insurance company. Therefore, the interest rate is more important than the death rate in determining the premium. The research on the stochastic interest rate meets the needs of social development. More and more scholars are devoted to the study of the stochastic interest rate. With the increase of people's living cost, installment payment arises at the historic moment. When buying a house or a car, people can choose to pay monthly, but in the past life insurance was paid annually. Recently, a number of Chinese life insurance companies have introduced new life insurance, this new life insurance can be paid quarterly, even monthly. Therefore, this paper studies the actuarial model of life insurance by installment under random interest rate. This paper first introduces some basic concepts of stochastic process and actuarial model of life insurance. Secondly, using the Wiener process and the Poisson process to simulate the fluctuation of interest rate, the combined life insurance actuarial model under the stochastic interest rate is constructed, and the influence of inflation on the policy holder is analyzed, and the consumer price index is introduced into the actuarial model of life insurance. The actuarial model of life insurance is constructed. The net premium, equilibrium premium, liability reserve and loss risk of insurance company are derived. Thirdly, under the Gompertz hypothesis and UDD hypothesis, we simplify the life insurance model by installment, and obtain the corresponding expressions of the net premium, equilibrium pure premium, liability reserve and the loss risk of insurance company. Finally, the effects of the payment function, the number of installments and the insured period on the premium and liability reserve are analyzed by numerical calculation, and the stochastic interest rate model is tested according to the interest rate variation data over the years. The model can not only reduce the insurance premium but also reduce the loss risk of the insurance company. The model has practical application value.
【学位授予单位】：哈尔滨工程大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：F840.62;O211

【参考文献】