中文摘要：

对于年金的定价问题的研究，传统精算理论假定利率是恒定不变的．但事实上，由于受到多种因素的影响，利率往往具有不确定性．因此，本文采用可逆MA（1）模型来刻画利率期限机构，在此基础上，研究了期末付倒平顶虹式年金的各阶矩问题，推导出了其年金现值的期望和方差的简洁公式．通过数值模拟分析了此年金面临的利率风险，其结论对年金定价有一定的参考价值．

英文摘要：

In the research of annuity pricing, interest rate is usually assumed to be constant in traditional actuarial theory. However, it is often uncertain for various factors. In this paper, the term structure of interest rate is modeled by adopting reversible MA（ 1 ） , based on which, the moment of the final flatheaded rainbow - payment - annuity is studied, and simple formulas for the expectation and variance of present value are given. By numerical simulation, interest rate risk of such annuity is analyzed, the final conclusion of which provides a reference to annuity pricing.