Research On The Theory Of Annuities Under Random Rates Of Interest

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.