# 指数分布利息力下年金的期望和方差The Expectation and Variance of Annuity under Exponential Distributed Interest Force

Abstract:
An annuity is a series of cash flow within a certain period of time. The present value of the annuity is closely related to interest rates. In the traditional actuarial theory, the interest rate is usually assumed to be fixed and known in advance in the calculation of the annuity. This assumption basically is mathematically treated easily and hypothetical. However, the actual interest rate is dependent on investment income, exchange rate, financial market and other factors. Therefore, it is more reasonable to assume that the interest rate is a random variable. In this paper, the interest force is assumed to be exponentially distributed, and correspondingly, the expectation and variance of the various fixed annuities and life annuities are hence derived.

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