随机贴现率下的年金

Annuities Under Random Rates of Discount

对于随机利率下的年金,已经有了一些研究成果[2～4],在[2]中,AbrahamZaks推导了简单递增年金的现值.本文在假设各年度的贴现率在一定时期内为相互独立、且有相同期望和方差的随机变量的情况下,对几种确定年金———基本年金和简单递减年金———的现值进行了深入研究,求出了这几种简单年金的期望和方差,其中主要运用了数学归纳法.事实上,对于其它形式的年金也可以做类似研究.

As for annuities under random rates of interest, there were several excellent results. In , Abraham Zaks investigated the present value of increasing annuitydeferred. This paper investigate the present value of some annuitiescertain in which the rates of discount are independent random variables with the same expected value and variance. The expected value and the variance of the present value of some simple anuities, such as single payment and series of level payments and decreasing annuityimmediate, are derived. We use the method of induction. Other cases can be done similarly.