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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。
Because life tables provide only life function values and mortality values at integer age points, non-integer age assumptions are required when calculating survival function values at non-integer ages in demographic and life insurance actuarial. The traditional non-integer age hypothesis has the shortcomings that the death force function and the density function jump greatly at integer ages, while the improvement to their continuity is very little, and there is no research on the quadratic polynomial form of the death force function. In this paper, the quadratic polynomial form of death force is proposed, and the non-integer age hypothesis corresponding to quadratic polynomial death force form is given by the piecewise parabolic interpolation method under integral constraints. The hypothesis is compared with the assumptions that have been made by the predecessors The results show that the second death force hypothesis can describe the survival model more accurately, so as to make the calculation of the annuity and demographic and annuity more accurate.