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中文摘要：
研究在随机利率相互独立条件下年金初值的计算问题，主要是研究各类年金初值的期望和方差的计算公式．文章给出了随机利率相互独立条件下期末付平顶虹式年金，期末付虹式年金，期末付倒平顶虹式年金和期末付倒虹式年金的初值公式及其简化关系，推导出了这类年金初值的各阶矩的简化公式，进而获得了这类年金初值的期望计算公式和方差计算公式．
英文摘要：
It is mainly to study the mathematical expectation and variance of the present value of some annuities about the calculation under stochastic interest rates. In this paper, we give the present values of some annuities whose paymentsare of the flatheaded rainbow, the rainbow,the reverse flatheaded rainbow and the reverse rainbow and derive the simplified formulas under stochastic interest rates. The simplified formulas of the moment of the present values of the annuities are derived, and the expectation and variance of these annuities are obtained.
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