随机利率下现值函数的极限分布及其上、下界

The Limiting Distribution of Present Value Function and Its Upper and Lower Bounds Under Stochastic Rate of Interest

考虑在随机利率情形下由n个同质的被保人所组成的终身寿险组合的现值函数。在各被保人的未来余命随机变量相互独立的情形下,得到了现值函数的极限分布。并进一步考虑采用Dhaene等人所研究的Comonotonicity方法,给出了现值函数极限分布的上、下凸界。文章最后给出了一个数值模拟说明其主要结果。

In this paper, we consider the present value function of a homogeneous portfolio composed by n whole life insurance policies under the stochastic interest rate. Specifically, we obtain the limiting distribution of the present value function under the independence assumption among the future-lifetime random variables of the insured. Moreover, we obtain the upper and lower convex bounds of the limiting distribution in general case by introducing the concept of comonotonicity according to Dhaene et al.Finally, a numerical simulation is presented to illustrate the main result in our paper.