随机利率下的净保费责任准备金

在传统的精算定价模型中，都采用固定利率来计算净保费及净保费责任准备金，这样利率的波动可能会导致保险公司利润的减少，甚至会给其带来无法预计的风险．为建立一个能够规避利率波动风险的精算模型，同时研究随机利率下保险公司的损失风险，首先利用Wiener过程对随机利率建模，再将其引入传统的精算模型，最后推导出随机利率下，终身寿险的净保费和净保费责任准备金的一般表达式，并在此基础上进一步得出保险公司在各个时刻损失风险的一般表达式．实例表明，净保费责任准备金随着时间的增长不断增加，而公司的损失风险会不断减小．

Net premium reserve of stochastic interest

In the traditional actuarial model, net premium and net premium reserves are calculated at fixed interest rates. However, the fluctuation of fixed interest rates affects the insurance company greatly and can lead to disasterous results. It is necessary to establish a model which can eliminate the effect of interest fluctuation and also can study the loss risk of insurer at the stochastic interest. The Wiener process is used to model the stochastic interest rates and then it is introduced to the traditional actuarial model. The formulas of net premium and net premium reserve of life insurance are approached, and the formulas of loss risk of the insurance company at every moment are also deduced. By an actual example, it is concluded that the reserve is increasing by the time and the loss risk is decreasing at the same time.