IDEAS home Printed from https://ideas.repec.org/a/eee/insuma/v50y2012i2p229-235.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167668711001314
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.insmatheco.2011.11.009?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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. Esther Frostig, 2002. "Comparison Between Future Lifetime Distribution and Its Approximations," North American Actuarial Journal, Taylor & Francis Journals, vol. 6(2), pages 11-17.
    4. 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.
    5. Frostig, Esther, 2003. "Properties of the power family of fractional age approximations," Insurance: Mathematics and Economics, Elsevier, vol. 33(1), pages 163-171, August.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. 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.
    3. 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).
    4. Lee, Hangsuck & Ahn, Jae Youn & Ko, Bangwon, 2019. "Construction of multiple decrement tables under generalized fractional age assumptions," Computational Statistics & Data Analysis, Elsevier, vol. 133(C), pages 104-119.
    5. 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.
    6. Frostig, Esther, 2003. "Properties of the power family of fractional age approximations," Insurance: Mathematics and Economics, Elsevier, vol. 33(1), pages 163-171, August.
    7. Yi, Zhang & Weng, Chengguo, 2006. "An application of the [alpha]-power approximation in multiple life insurance," Insurance: Mathematics and Economics, Elsevier, vol. 38(1), pages 98-112, February.
    8. 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.
    9. Dahan, Merav & Frostig, Esther & Langberg, Naftali A., 2003. "Analysis of heterogeneous endowment policies portfolios under fractional approximations," Insurance: Mathematics and Economics, Elsevier, vol. 33(3), pages 567-584, December.
    10. Shilong Li & Xia Zhao & Nailong Guo, 2013. "Fractional mortality rate based on rational interpolating method and its application in actuarial science," Quality & Quantity: International Journal of Methodology, Springer, vol. 47(2), pages 791-802, February.
    11. S. Nadarajah & S. Bakar, 2013. "A new R package for actuarial survival models," Computational Statistics, Springer, vol. 28(5), pages 2139-2160, October.
    12. 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.
    13. Lee, Hangsuck & Ha, Hongjun & Lee, Taewon, 2021. "Decrement rates and a numerical method under competing risks," Computational Statistics & Data Analysis, Elsevier, vol. 156(C).

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:insuma:v:50:y:2012:i:2:p:229-235. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/505554 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.