基于有理样条死亡假设的分数时点寿险净保费责任准备金

Fractional Net Premium Reserve in Life Insurance Based on Rational Interpolation Method

保险责任准备金是保险公司风险管理的重要度量指标,责任准备金的精确合理的测算,将会对保险公司的健康发展起着极其重要的作用。分数时点净保费责任准备金的测算依赖于精算假设,本文在提出一类有理样条死亡假设的基础上,研究了终身寿险的分数时点净保费责任准备金的计算问题。我们得到了其理论计算公式和上下界范围,探讨了调节参数的变化对净保费责任准备金的影响。数据分析表明:分数时点责任准备金对调节参数的变化比较敏感,目前常用的UDD假设下的责任准备金测算值恰是本文方法下的一个边界。所以基于有理样条估计方法的分数时点责任准备金测算在实务中具有很强的灵活性,对保险公司责任准备金风险管理具有重要的指导意义。

In the risk management of insurance companies, insurance reserve is an important measure index. It is very important for the healthy development of insurance companies to calculate the premium reserve precisely and reasonably. Because the calculation of the net premium reserve at a fractional age depends on the actuarial assumption, this paper attempts to discuss the net premium reserve at the fractional age of the whole life insurance based on a rational spline method for estimating the mortality of fractional ages. In this discussion, the calculation formula and the bounds range of the net premium reserve at the fractional ages are obtained; Furthermore, we analyze the influence of the change of the adjustable parame- ter on the net premium reserve. The data analysis shows that not only it is sensitive for the net premium reserve at the fractional age to change the adjustable parameter, but also this reserve value based on the UDD assumption is just a boundary value using our method. So the calculation of the net premium reserves at the fractional ages based on rational spline method is very flexible, and it also has the important guiding significance for the risk management of the insurance reserve.