一类随机利率下的增额寿险模型

A Class of Models about Increasing Payments Life Insurance under the Stochastic Interest

对寿险中的利率随机性问题的研究是近几年来保险精算研究的热点和重点问题之一，本文以即时给付的一类增额寿险为对象，考虑到突发事件对利率的影响，对随机利率采用Ｇａｕｓｓ过程与Ｐｏｉｓｓｏｎ过程联合建模，给出即时给付的增额寿险的给付现值的各阶矩，并在一些特殊条件下给出矩的简洁表达式。

The study of interest randomness is one of the heated and major problems of actuarial science in recent years. In this paper, giving a class of increasing payments life insurance and considing abrupt event's effect on interest, we establish the model for stochastic interest jointly by both Gauss process and Poisson process, and give all orders moment of payable present value of immediately payable increasing life insurance. Finally, the concise expressions are given in some special cases.