随机利息力下的一类年金的时间价值

Time Value of a Class of Annuities with Stochastic Interest Force

对于年金的时间价值的研究,往往假定利率在整个期间内是固定不变的.但事实上,由于受到多种因素的影响,利率通常具有不确定性.因此,本文采用可逆MA(1)模型对随机利息力进行建模,在此基础上,研究了期末付虹式年金和期末付平顶虹式年金的时间价值问题,给出了上述两种形式年金现值的期望和方差的递推公式.通过数值仿真分析了相关参数对期末付虹式年金现值的期望值的影响,其结论对投资者的投资决策提供了参考依据.

In the research of time value of annuities,interest rate is usually assumed to be constant throughout the whole period.However,it is often uncertain for various factors.In this paper,the stochastic interest force was modeled by adopting reversible MA（1）,and based on this,the time value of final rainbow-payment-annuity and final flatheaded rainbow-payment-annuity were studied,thus the formulas for the expectation and variance of present value were given.By numerical simulation,the influence of relevant parameters on the expectation of present value of final rainbow-payment-annuity was analyzed,which provides a reference to investors in making investment decisions.