IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v133y2019icp104-119.html
   My bibliography  Save this article

Construction of multiple decrement tables under generalized fractional age assumptions

Author

Listed:
  • Lee, Hangsuck
  • Ahn, Jae Youn
  • Ko, Bangwon

Abstract

In this paper, we intend to develop a consistent methodology for constructing multiple decrement tables under generalized fractional age assumptions. Assuming that decrements have a common distribution at fractional ages, we derive conversion formulas to split or merge given multiple decrement tables in order to obtain a new multiple decrement table of interest. The assumptions that we consider are quite general, with a wide range of fractional age assumptions including the uniform distribution of decrements or the constant forces of decrement. Our proposed approaches allow us to directly obtain multiple decrement tables without the need for the associated single rates of decrement. They will also enable us to avoid potential inconsistency under the uniform distribution assumptions or unnaturalness arising from the constant forces assumption. In addition, as they navigate through a larger window, they will deepen our understanding of the classical results under the uniform distribution assumptions. Although our methodology is based on a common distribution function assumption, knowing the specific form of the function is unnecessary, since our conversion formulas do not depend upon it. Finally, numerical examples are illustrated where we investigate the main factors of the errors induced by the discrepancy between the true and assumed distributions. The numerical result shows that the relative errors under our approaches are practically negligible for moderate ranges of multiple decrement probabilities.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:csdana:v:133:y:2019:i:c:p:104-119
    DOI: 10.1016/j.csda.2018.09.004
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947318302329
    Download Restriction: Full text for ScienceDirect subscribers only.

    File URL: https://libkey.io/10.1016/j.csda.2018.09.004?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. Dickson,David C. M. & Hardy,Mary R. & Waters,Howard R., 2013. "Solutions Manual for Actuarial Mathematics for Life Contingent Risks," Cambridge Books, Cambridge University Press, number 9781107620261, February.
    2. Gordon Willmot, 1997. "Statistical Independence and Fractional Age Assumptions," North American Actuarial Journal, Taylor & Francis Journals, vol. 1(1), pages 84-90.
    3. 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.
    4. Dickson,David C. M. & Hardy,Mary R. & Waters,Howard R., 2013. "Actuarial Mathematics for Life Contingent Risks," Cambridge Books, Cambridge University Press, number 9781107044074, October.
    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.
    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. Lee, Hangsuck & Ha, Hongjun & Lee, Taewon, 2021. "Decrement rates and a numerical method under competing risks," Computational Statistics & Data Analysis, Elsevier, vol. 156(C).

    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. 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.
    2. Frostig, Esther, 2003. "Properties of the power family of fractional age approximations," Insurance: Mathematics and Economics, Elsevier, vol. 33(1), pages 163-171, August.
    3. Raj Kumari Bahl & Sotirios Sabanis, 2017. "General Price Bounds for Guaranteed Annuity Options," Papers 1707.00807, arXiv.org.
    4. Thomas Bernhardt & Catherine Donnelly, 2019. "Modern tontine with bequest: innovation in pooled annuity products," Papers 1903.05990, arXiv.org.
    5. 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.
    6. Barigou, Karim & Goffard, Pierre-Olivier & Loisel, Stéphane & Salhi, Yahia, 2023. "Bayesian model averaging for mortality forecasting using leave-future-out validation," International Journal of Forecasting, Elsevier, vol. 39(2), pages 674-690.
    7. Carole Bernard & Adam Kolkiewicz & Junsen Tang, 2023. "Valuation of Reverse Mortgages with Default Risk Models," The Journal of Real Estate Finance and Economics, Springer, vol. 66(4), pages 806-839, May.
    8. 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.
    9. Bernhardt, Thomas & Donnelly, Catherine, 2019. "Modern tontine with bequest: Innovation in pooled annuity products," Insurance: Mathematics and Economics, Elsevier, vol. 86(C), pages 168-188.
    10. 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).
    11. Landriault, David & Moutanabbir, Khouzeima & Willmot, Gordon E., 2015. "A note on order statistics in the mixed Erlang case," Statistics & Probability Letters, Elsevier, vol. 106(C), pages 13-18.
    12. Zhou, Rui & Li, Johnny Siu-Hang & Tan, Ken Seng, 2015. "Modeling longevity risk transfers as Nash bargaining problems: Methodology and insights," Economic Modelling, Elsevier, vol. 51(C), pages 460-472.
    13. He, Lin & Liang, Zongxia & Yuan, Fengyi, 2020. "Optimal DB-PAYGO pension management towards a habitual contribution rate," Insurance: Mathematics and Economics, Elsevier, vol. 94(C), pages 125-141.
    14. Jin Sun & Eckhard Platen, 2019. "Benchmarked Risk Minimizing Hedging Strategies for Life Insurance Policies," Research Paper Series 399, Quantitative Finance Research Centre, University of Technology, Sydney.
    15. Deelstra, Griselda & Grasselli, Martino & Van Weverberg, Christopher, 2016. "The role of the dependence between mortality and interest rates when pricing Guaranteed Annuity Options," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 205-219.
    16. Manuel L. Esquível & Gracinda R. Guerreiro & Matilde C. Oliveira & Pedro Corte Real, 2021. "Calibration of Transition Intensities for a Multistate Model: Application to Long-Term Care," Risks, MDPI, vol. 9(2), pages 1-17, February.
    17. Wang, Suxin & Lu, Yi & Sanders, Barbara, 2018. "Optimal investment strategies and intergenerational risk sharing for target benefit pension plans," Insurance: Mathematics and Economics, Elsevier, vol. 80(C), pages 1-14.
    18. 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.
    19. He, Lin & Liang, Zongxia & Wang, Sheng, 2022. "Dynamic optimal adjustment policies of hybrid pension plans," Insurance: Mathematics and Economics, Elsevier, vol. 106(C), pages 46-68.
    20. Marius D. Pascariu & Ugofilippo Basellini & José Manuel Aburto & Vladimir Canudas-Romo, 2020. "The Linear Link: Deriving Age-Specific Death Rates from Life Expectancy," Risks, MDPI, vol. 8(4), pages 1-18, October.

    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:csdana:v:133:y:2019:i:c:p:104-119. 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/csda .

    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.