非整数年龄假设中的二次多项式死亡力研究

由于生命表只提供了整数年龄点上的生存函数值和死亡率值,所以在人口统计和寿险精算中计算非整数年龄处的生存函数值时,需要进行非整数年龄假设。传统的非整数年龄假设有死亡力函数和密度函数在整数年龄处有较大跳跃的缺点,而针对它们连续性的改进甚少,且没有针对死亡力函数二次多项式形式的研究。本文提出了死亡力的二次多项式形式,通过积分约束下的分段抛物插值方法给出了二次多项式死亡力形式对应的非整数年龄假设,并与前人已经提出的各种假设进行了比较,结果表明二次死亡力假设可以更精确地描述生存模型,从而使人口统计和保费、年金的计算更加精确。

Research on Quadratic Force of Mortality in Fractional Age Assumption

Life tables usually show the survival function and mortality of exact integer ages,so fractional age assumptions are necessary in the calculation of survival functions on fractional ages in demography and life contingencies.Traditional fractional age assumptions have the defect of implausible discontinuities at integer ages;however,there are few documents on improving them,and no research on quadratic force of mortality.This paper will introduce the quadratic form of force of mortality;derive the fractional age assumption corresponding to quadratic force of mortality by the methods of piecewise parabolic interpolation under integral constraint;compare this assumption with other assumptions introduced before.The result shows that life models can be described more accurately by quadratic force of mortality assumption,so population statistics and calculation of premiums,actuarial present values of annuities can be more accurate.