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Comparison Between Future Lifetime Distribution and Its Approximations

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  • Esther Frostig

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.

Suggested Citation

  • Esther Frostig, 2002. "Comparison Between Future Lifetime Distribution and Its Approximations," North American Actuarial Journal, Taylor & Francis Journals, vol. 6(2), pages 11-17.
    • Handle: RePEc:taf:uaajxx:v:6:y:2002:i:2:p:11-17
    DOI: 10.1080/10920277.2002.10596040
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    Cited by:

    1. Tsai, Cary Chi-Liang & Jiang, Lingzhi, 2011. "Actuarial applications of the linear hazard transform in life contingencies," Insurance: Mathematics and Economics, Elsevier, vol. 49(1), pages 70-80, July.
    2. Christiansen, Marcus & Denuit, Michel, 2012. "Worst-case actuarial calculations consistent with single- and multiple-decrement life tables," LIDAM Discussion Papers ISBA 2012027, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    3. Jose M. Pavía & Josep Lledó, 2022. "Estimation of the combined effects of ageing and seasonality on mortality risk: An application to Spain," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 185(2), pages 471-497, April.
    4. Barz, Christiane & Müller, Alfred, 2012. "Comparison and bounds for functionals of future lifetimes consistent with life tables," Insurance: Mathematics and Economics, Elsevier, vol. 50(2), pages 229-235.

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