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

摘要: 年金是指在一定期限内的系列现金流量。年金的现值与利率密切相关。在传统的精算理论中，在年金的计算中，常常假定利息率为已知的非随机变量，这主要是数学上处理的方便而假设的。然而，实际中的利息率与投资收益、汇率、金融市场等多种因素有关，假定利息率是随机变量更加合理。本文在利息力指数分布的模型子下，研究了各种固定年金和生存年金的期望和方差。

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.