研究在随机贴现率相互独立条件下某些延付年金现值的计算问题,目的在于研究其现值的期望和方差.本文重新定义了在固定贴现率下的一系列延付年金的现值公式,并给出了在随机贴现率相互独立条件下某些年内期末付等额年金,递增年金,递减年金和几何级数年金的现值计算公式及其现值的一阶矩、二阶矩的递推关系.利用该关系,推导出了各年金现值的期望和方差公式.
The calculation of present value of some annuities is investigated over a period of years in which the rate of discount is a random variable under some restrictions and focus on the expected value and variance of the present value. Some formulas of the present value whose rate of discount is fixed are given firstly. Meanwhile, the relationships for the moment of the present values is found and solved. Using these relations, the mean and variance of the present values are derived.