Abstract: 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 parameter 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.

Key words: rational interpolating method, fractional age, net premium reserves, adjustable parameter