随机利率下的寿险模型研究

文档编号:XXLW075 文档字数:6074,页数:22

摘  要
 为了能让理论更加符合实际，使精算模型更好地贴近保险实务，文中以死亡年末支付1个单位赔付的n年定期寿险为研究对象，以更符合实际情况的随机利率为研究目标，对传统精算模型进行改进，以求出更实际化的结果，使理论成果与实际情况做到最大化的接近。首先按固定利率求出赔付现值的期望值，即趸缴纯保费作为参照组。其次用随机利率代替固定利率，并用Wiener过程对利息力建立随机模型，通过随机过程的分布性质来确定利息力积累函数的期望值，从而得出该种类寿险在随机利率情况下的趸缴纯保费，并与参照组比较，通过实例计算得到最终结果，分析随机利率对该种类寿险的趸缴纯保费的影响程度。

关键词：随机利率  定期寿险  趸缴纯保费  Wiener过程

Abstract
 For the theory in line with the actual much more and the actuarial model closes to insurance practice better, this article researches n years’ term life insurance which pays 1 unit at the end of death of the insured person as the object, and researches stochastic interest rate which links the actual situation more closely as the target, then improves the traditional actuarial model to work out result more realistic and makes the maximize approach between the theoretic achievement and the practice circumstance. Firstly, we compute the expect value of present value of payment (i.e. net single premium) under fixed interest rate as the reference group. Subsequently, utilise stochastic interest rate substitute for the fixed interest rate, and sets a random model about interest force by Wiener process, then makes sure the expect value of accumulation function of interest force through the character of distribution of stochastic process, from what we can get the net single premium of this kind of life insurance under stochastic interest rate. Through comparing with the reference group above and computing the final result with example, we can analyze and gain the impact level of the stochastic interest rate affects the net single premium of this kind of life insurance.

Key words: Stochastic interest rate; Term life insurance; Net single premium; Wiener process
  
目  录
摘  要 I
Abstract II
目  录 III
第一章    引言 1
1.1    随机利率下的寿险模型研究的背景与意义 1
1.2    主要研究内容及拟解决的问题 2
1.3    解决问题的研究方法 2
第二章    相关基础知识 3
2.1    保险精算学中的部分符号阐释 3
2.2    Wiener过程 4
2.2.1  Wiener过程的定义 4
2.2.2  Wiener过程的性质 5
第三章    n年定期寿险的趸缴纯保费 7
3.1    固定利率下的趸缴纯保费 7
3.2    随机利率下的趸缴纯保费 7
第四章    随机利率对趸缴纯保费的影响 10
4.1    实例分析 10
4.2    随机利率对趸缴保费的影响程度 11
第五章    结束语 13
致  谢 14
参考文献 15
附录一 16
附录二 19

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