Annuities Under A Kind Of Random Rates Of Interest

In the traditional annuity, it was mostly supposed that the interest is permenant in order to simplify the calculate. Therefore, life insurance is the economic performance of a long period of time. Many facts, such as policy of government, economic circles, can cause the uncertainty of interest during the time of insurance. Thus, the research and calculation of life insurance under the random interest is focused these years.In this paper, wo focused on the annuity under random interest, and do the research of two kinds of models of interest, calculate the expected accumulated value of the annuity under the two assumptions. Suppose interest perform as the stochastic process i_k = i_k-1+η_k or i_t = (1+η_t)i_t-1, where is the interest of kth year and represent the stochastic variant of a certain distribution. Wo discussed both models and got the fomular of expected accumulated value. In addition, under the AR(1) model, we dispersed the state space and did many numerical work. At last, we use amounts of historical data to check the veracity of the models.