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Comparison and bounds for functionals of future lifetimes consistent with life tables

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  • Barz, Christiane
  • Müller, Alfred

Abstract

We derive a new crossing criterion of hazard rates to identify a stochastic order relation between two random variables. We apply this crossing criterion in the context of life tables to derive stochastic ordering results among three families of fractional age assumptions: the family of linear force of mortality functions, the family of quadratic survival functions and the power family. Further, this criterion is used to derive tight bounds for functionals of future lifetimes that exhibit an increasing force of mortality with given one-year survival probabilities. Numerical examples illustrate our findings.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:insuma:v:50:y:2012:i:2:p:229-235
    DOI: 10.1016/j.insmatheco.2011.11.009
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    References listed on IDEAS

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    1. Gordon Willmot, 1997. "Statistical Independence and Fractional Age Assumptions," North American Actuarial Journal, Taylor & Francis Journals, vol. 1(1), pages 84-90.
    2. Jones, Bruce L. & Mereu, John A., 2000. "A family of fractional age assumptions," Insurance: Mathematics and Economics, Elsevier, vol. 27(2), pages 261-276, October.
    3. Frostig, Esther, 2003. "Properties of the power family of fractional age approximations," Insurance: Mathematics and Economics, Elsevier, vol. 33(1), pages 163-171, August.
    4. Esther Frostig, 2002. "Comparison Between Future Lifetime Distribution and Its Approximations," North American Actuarial Journal, Taylor & Francis Journals, vol. 6(2), pages 11-17.
    5. Jones, Bruce L. & Mereu, John A., 2002. "A critique of fractional age assumptions," Insurance: Mathematics and Economics, Elsevier, vol. 30(3), pages 363-370, June.
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    Cited by:

    1. Christiansen, Marcus C. & Denuit, Michel M., 2013. "Worst-case actuarial calculations consistent with single- and multiple-decrement life tables," Insurance: Mathematics and Economics, Elsevier, vol. 52(1), pages 1-5.
    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).

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    More about this item

    Keywords

    C02; IM10; IB11; Stochastic order; Fractional age assumptions; Increasing mortality rate; Bounds;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics

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