Comparison Between Future Lifetime Distribution and Its Approximations

Abstract

Life tables contain data on survival probabilities only for integral ages. The actuarial literature offers several approximation schemes to evaluate survival probabilities for nonintegral ages: the uniform, exponential, and Balducci approximations. This paper shows that, if the real survival model has an increasing hazard rate, the last two approximations are stochastically smaller than the real survival model. Conditions are given on the real survival model, under which it is smaller in convex ordering than the uniform approximation. The paper shows how this result can be applied to give bounds on continuous whole life insurance and whole life annuity. It also investigates the kinds of dependency between the integral part of the lifetime and the fractional portion of the lifetime in the exponential and Balducci approximations.

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