【作者】 刘凌晨；

【导师】 杨大地；

【作者基本信息】 重庆大学 ， 计算数学， 2007， 硕士

【摘要】 传统的精算理论假定利率是确定的,事实上利率具有随机性。随着精算理论研究的深入,利率随机性的研究在近20年来已逐步受到重视,且已成为近年来保险精算研究的热点问题之一。关于随机利率下的年金的计算问题,许多专家作了专门的讨论。目前,关于研究离散时间下的随机利率在一定的约束条件下的一类年金的现值或积累值的计算问题,主要是计算年金现值或积累值的期望和方差。本文取得的结果可概括如下:(1)首次将随机利率引入期末付虹式年金,期末付平顶虹式年金,期末付倒虹式年金和期末付倒平顶虹式年金。(2)从随机利率出发,主要对随机利率下的期末付虹式年金和期末付平顶虹式年金进行详细的分析和研究,推出对应年金的初值和积累值的期望和方差的计算方法。其次是研究方差的递推关系,给出计算公式,这对于深入和完善随机利率在年金中的应用有着深刻理论意义和实际意义。更多还原

【Abstract】 In traditional actuarial theory, for simplicity, it is assumed that underlying interest rate is fixed and the same for all years. However, the interest rate that will apply in future years is of course neither known nor constant. Many experts have made discussions on the calculation of annuity with random rates of interest.Currently, many experts have investigated present or accumulated values of annuities-certain with yearly payments with independent random interest rates. They consider the calculation of present value or accumulated of some annuities over a period of years in which the rate of interest is a random variable under some restrictions,and aim at the expected value and variance of the present value or accumulated.The main works obtained here can be summarized as follows:(1) The random interest rates are firstly introduced into the flatheaded rainbow annuity-immediate, the rainbow annuity-immediate, the reverse flatheaded rainbow annuity-immediate and the reverse rainbow annuity-immediate.(2) In this paper, some special patterns of annuity changes whose payments are of the flatheaded rainbow annuity-immediate, the rainbow annuity-immediate, the reverse flatheaded rainbow annuity-immediate and the reverse rainbow annuity-immediate are studied, and beginning or accumulated values are given. Meanwhile, we find recursive relationships for the variance of the present value or accumulated,and solve these relationships.更多还原