CIR利率模型下永久年金现值变量的分布模拟  

Simulation of the present value of perpetuity in CIR interest model

作　　者：张连增[1] 段白鸽[2] 

机构地区：[1]南开大学经济学院风险管理与保险学系,天津300071 [2]复旦大学经济学院风险管理与保险学系,上海200433

出　　处：《系统工程学报》2014年第1期56-65,共10页Journal of Systems Engineering

基　　金：国家自然科学基金资助项目(71271121);中央高校基本科研业务费专项资金资助项目(NKZXTD1101)

摘　　要：考虑利息力过程是CIR过程的永久年金,首先给出永久年金现值变量均值的解析解,其中涉及到超几何函数2F1,进一步给出永久年金现值变量二阶矩的上界,并应用Mathematica软件给出了数值解.最后,应用R软件模拟了CIR模型下永久年金现值变量的分布.对于永久年金现值变量的均值,由随机模拟得到的分布均值与根据解析解计算的均值非常接近.When the force of interest is a CIR process, the analytical expression for the distribution of present value of perpetuity is difficult to obtain. In this paper we consider the perpetuity when the force of interest is a CIR process. First, we provide with the explicit expression for the mean of the present value of perpetuity using the hypergeometric function 2F1. Then we provide with an upper bound for the second moment of perpetuity in CIR model. Using the software Mathematica, numerical results are provided. As a benchmark, the present value of perpetuity in the CIR model is simulated, which is implemented with the R software. For the mean of the present value of perpetuity, the simulated results fit very well to the analytical solution.

关 键 词：永久年金 现值变量 CIR模型 随机模拟 

分 类 号：F830[经济管理—金融学]