IDEAS home Printed from https://ideas.repec.org/a/eee/insuma/v92y2020icp147-161.html
   My bibliography  Save this article

Calibrating Gompertz in reverse: What is your longevity-risk-adjusted global age?

Author

Listed:
  • Milevsky, Moshe A.

Abstract

This paper develops a computational framework for inverting Gompertz–Makeham mortality hazard rates, consistent with compensation laws of mortality for heterogeneous populations, to define a longevity-risk-adjusted global (L-RaG) age. To illustrate its salience and possible applications, the paper calibrates and presents L-RaG values using country data from the Human Mortality Database (HMD). Among other things, the author demonstrates that when properly benchmarked, the longevity-risk-adjusted global age of a 55-year-old Swedish male is 48, whereas a 55-year-old Russian male is closer in age to 67. The paper also discusses the connection between the proposed L-RaG age and the related concept of Biological age, from the medical and gerontology literature. Practically speaking, in a world of growing mortality heterogeneity, the L-RaG age could be used for pension and retirement policy. In the language of behavioral finance and economics, a salient metric that adjusts chronological age for longevity risk might help capture the public’s attention, educate them about lifetime uncertainty and induce many of them to take action — such as working longer and/or retiring later.

Suggested Citation

  • Milevsky, Moshe A., 2020. "Calibrating Gompertz in reverse: What is your longevity-risk-adjusted global age?," Insurance: Mathematics and Economics, Elsevier, vol. 92(C), pages 147-161.
  • Handle: RePEc:eee:insuma:v:92:y:2020:i:c:p:147-161
    DOI: 10.1016/j.insmatheco.2020.03.009
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167668720300445
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.insmatheco.2020.03.009?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. Willemse, W.J. & Kaas, R., 2007. "Rational reconstruction of frailty-based mortality models by a generalisation of Gompertz' law of mortality," Insurance: Mathematics and Economics, Elsevier, vol. 40(3), pages 468-484, May.
    2. Chen, An & Vigna, Elena, 2017. "A unisex stochastic mortality model to comply with EU Gender Directive," Insurance: Mathematics and Economics, Elsevier, vol. 73(C), pages 124-136.
    3. Melnikov, Alexander & Romaniuk, Yulia, 2006. "Evaluating the performance of Gompertz, Makeham and Lee-Carter mortality models for risk management with unit-linked contracts," Insurance: Mathematics and Economics, Elsevier, vol. 39(3), pages 310-329, December.
    4. Donnelly, Catherine & Guillén, Montserrat & Nielsen, Jens Perch, 2014. "Bringing cost transparency to the life annuity market," Insurance: Mathematics and Economics, Elsevier, vol. 56(C), pages 14-27.
    5. Valdez, Emiliano A. & Vadiveloo, Jeyaraj & Dias, Ushani, 2014. "Life insurance policy termination and survivorship," Insurance: Mathematics and Economics, Elsevier, vol. 58(C), pages 138-149.
    6. 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.
    7. Hainaut, Donatien, 2016. "Impact of volatility clustering on equity indexed annuities," LIDAM Reprints ISBA 2016045, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    8. Hainaut, Donatien, 2016. "Impact of volatility clustering on equity indexed annuities," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 367-381.
    9. Shapiro, Arnold F., 2013. "Modeling future lifetime as a fuzzy random variable," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 864-870.
    10. Luciano, Elisa & Regis, Luca, 2014. "Efficient versus inefficient hedging strategies in the presence of financial and longevity (value at) risk," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 68-77.
    11. Meyricke, Ramona & Sherris, Michael, 2013. "The determinants of mortality heterogeneity and implications for pricing annuities," Insurance: Mathematics and Economics, Elsevier, vol. 53(2), pages 379-387.
    12. Feng, Runhuan & Yi, Bingji, 2019. "Quantitative modeling of risk management strategies: Stochastic reserving and hedging of variable annuity guaranteed benefits," Insurance: Mathematics and Economics, Elsevier, vol. 85(C), pages 60-73.
    13. X. Lin & Xiaoming Liu, 2007. "Markov Aging Process and Phase-Type Law of Mortality," North American Actuarial Journal, Taylor & Francis Journals, vol. 11(4), pages 92-109.
    14. Jevtić, Petar & Luciano, Elisa & Vigna, Elena, 2013. "Mortality surface by means of continuous time cohort models," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 122-133.
    15. Donnelly, Catherine & Guillén, Montserrat & Nielsen, Jens Perch, 2013. "Exchanging uncertain mortality for a cost," Insurance: Mathematics and Economics, Elsevier, vol. 52(1), pages 65-76.
    16. Huang, H. & Milevsky, M.A. & Salisbury, T.S., 2017. "Retirement spending and biological age," Journal of Economic Dynamics and Control, Elsevier, vol. 84(C), pages 58-76.
    17. Dahl, Mikkel, 2004. "Stochastic mortality in life insurance: market reserves and mortality-linked insurance contracts," Insurance: Mathematics and Economics, Elsevier, vol. 35(1), pages 113-136, August.
    18. Angoshtari, Bahman & Bayraktar, Erhan & Young, Virginia R., 2016. "Minimizing the probability of lifetime drawdown under constant consumption," Insurance: Mathematics and Economics, Elsevier, vol. 69(C), pages 210-223.
    19. Wang, Yumin, 2009. "Quantile hedging for guaranteed minimum death benefits," Insurance: Mathematics and Economics, Elsevier, vol. 45(3), pages 449-458, December.
    20. Gao, Huan & Mamon, Rogemar & Liu, Xiaoming & Tenyakov, Anton, 2015. "Mortality modelling with regime-switching for the valuation of a guaranteed annuity option," Insurance: Mathematics and Economics, Elsevier, vol. 63(C), pages 108-120.
    21. Milevsky, Moshe A., 2020. "Swimming with wealthy sharks: longevity, volatility and the value of risk pooling," Journal of Pension Economics and Finance, Cambridge University Press, vol. 19(2), pages 217-246, April.
    22. Cohen, Asaf & Young, Virginia R., 2016. "Minimizing lifetime poverty with a penalty for bankruptcy," Insurance: Mathematics and Economics, Elsevier, vol. 69(C), pages 156-167.
    23. Cairns, Andrew J.G. & Kallestrup-Lamb, Malene & Rosenskjold, Carsten & Blake, David & Dowd, Kevin, 2019. "Modelling Socio-Economic Differences In Mortality Using A New Affluence Index," ASTIN Bulletin, Cambridge University Press, vol. 49(3), pages 555-590, September.
    24. Ye, Zihan & Post, Thomas, 2020. "What age do you feel? – Subjective age identity and economic behaviors," Journal of Economic Behavior & Organization, Elsevier, vol. 173(C), pages 322-341.
    25. M. Govorun & B. L. Jones & X. Liu & D. A. Stanford, 2018. "Physiological Age, Health Costs, and Their Interrelation," North American Actuarial Journal, Taylor & Francis Journals, vol. 22(3), pages 323-340, July.
    26. Pitacco, Ermanno, 2004. "Survival models in a dynamic context: a survey," Insurance: Mathematics and Economics, Elsevier, vol. 35(2), pages 279-298, October.
    27. Fung, Man Chung & Ignatieva, Katja & Sherris, Michael, 2014. "Systematic mortality risk: An analysis of guaranteed lifetime withdrawal benefits in variable annuities," Insurance: Mathematics and Economics, Elsevier, vol. 58(C), pages 103-115.
    28. Moore, Kristen S., 2009. "Optimal surrender strategies for equity-indexed annuity investors," Insurance: Mathematics and Economics, Elsevier, vol. 44(1), pages 1-18, February.
    29. Ralph Stevens, 2017. "Managing Longevity Risk by Implementing Sustainable Full Retirement Age Policies," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 84(4), pages 1203-1230, December.
    30. Petrichev, Konstantin & Thorp, Susan, 2008. "The private value of public pensions," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 1138-1145, June.
    31. W.J. Willemse & R. Kaas, 2007. "Rational reconstruction of frailty-based mortality models by a generalisation of Gompertz' law of mortality," DNB Working Papers 135, Netherlands Central Bank, Research Department.
    32. Su, Shu & Sherris, Michael, 2012. "Heterogeneity of Australian population mortality and implications for a viable life annuity market," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 322-332.
    33. Haberman, Steven & Khalaf-Allah, Marwa & Verrall, Richard, 2011. "Entropy, longevity and the cost of annuities," Insurance: Mathematics and Economics, Elsevier, vol. 48(2), pages 197-204, March.
    34. John Payne & Namika Sagara & Suzanne Shu & Kirstin Appelt & Eric Johnson, 2013. "Life expectancy as a constructed belief: Evidence of a live-to or die-by framing effect," Journal of Risk and Uncertainty, Springer, vol. 46(1), pages 27-50, February.
    35. Andrés Villegas & Steven Haberman, 2014. "On the Modeling and Forecasting of Socioeconomic Mortality Differentials: An Application to Deprivation and Mortality in England," North American Actuarial Journal, Taylor & Francis Journals, vol. 18(1), pages 168-193.
    36. Menoncin, Francesco & Regis, Luca, 2017. "Longevity-linked assets and pre-retirement consumption/portfolio decisions," Insurance: Mathematics and Economics, Elsevier, vol. 76(C), pages 75-86.
    37. Luciano, Elisa & Regis, Luca & Vigna, Elena, 2012. "Delta–Gamma hedging of mortality and interest rate risk," Insurance: Mathematics and Economics, Elsevier, vol. 50(3), pages 402-412.
    38. Delong, Łukasz & Chen, An, 2016. "Asset allocation, sustainable withdrawal, longevity risk and non-exponential discounting," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 342-352.
    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. An Chen & Thai Nguyen & Thorsten Sehner, 2022. "Unit-Linked Tontine: Utility-Based Design, Pricing and Performance," Risks, MDPI, vol. 10(4), pages 1-27, April.
    2. Blake, David & Cairns, Andrew J.G., 2021. "Longevity risk and capital markets: The 2019-20 update," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 395-439.
    3. Mattia Mezzelani & Gloria Polinesi & Francesca Mariani & Maria Cristina Recchioni, 2021. "Longevity-risk-adjusted global age as a measure of well-being," RIEDS - Rivista Italiana di Economia, Demografia e Statistica - The Italian Journal of Economic, Demographic and Statistical Studies, SIEDS Societa' Italiana di Economia Demografia e Statistica, vol. 75(4), pages 28-30, October-D.
    4. Chen, An & Guillen, Montserrat & Rach, Manuel, 2021. "Fees in tontines," Insurance: Mathematics and Economics, Elsevier, vol. 100(C), pages 89-106.
    5. Chen, An & Rach, Manuel, 2023. "Actuarial fairness and social welfare in mixed-cohort tontines," Insurance: Mathematics and Economics, Elsevier, vol. 111(C), pages 214-229.

    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. Chen, An & Hieber, Peter & Rach, Manuel, 2021. "Optimal retirement products under subjective mortality beliefs," Insurance: Mathematics and Economics, Elsevier, vol. 101(PA), pages 55-69.
    2. Alvarez, Jesús-Adrián & Kallestrup-Lamb, Malene & Kjærgaard, Søren, 2021. "Linking retirement age to life expectancy does not lessen the demographic implications of unequal lifespans," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 363-375.
    3. Huang, Yiming & Mamon, Rogemar & Xiong, Heng, 2022. "Valuing guaranteed minimum accumulation benefits by a change of numéraire approach," Insurance: Mathematics and Economics, Elsevier, vol. 103(C), pages 1-26.
    4. Jesús-Adrián Álvarez & Malene Kallestrup-Lamb & Søren Kjærgaard, 2020. "Linking retirement age to life expectancy does not lessen the demographic implications of unequal lifespans," CREATES Research Papers 2020-17, Department of Economics and Business Economics, Aarhus University.
    5. Annamaria Olivieri & Ermanno Pitacco, 2016. "Frailty and Risk Classification for Life Annuity Portfolios," Risks, MDPI, vol. 4(4), pages 1-23, October.
    6. Blake, David & El Karoui, Nicole & Loisel, Stéphane & MacMinn, Richard, 2018. "Longevity risk and capital markets: The 2015–16 update," Insurance: Mathematics and Economics, Elsevier, vol. 78(C), pages 157-173.
    7. Anastasia Novokreshchenova, 2016. "Predicting Human Mortality: Quantitative Evaluation of Four Stochastic Models," Risks, MDPI, vol. 4(4), pages 1-28, December.
    8. Kirkby, J. Lars & Nguyen, Duy, 2021. "Equity-linked Guaranteed Minimum Death Benefits with dollar cost averaging," Insurance: Mathematics and Economics, Elsevier, vol. 100(C), pages 408-428.
    9. David Blake & Marco Morales & Enrico Biffis & Yijia Lin & Andreas Milidonis, 2017. "Special Edition: Longevity 10 – The Tenth International Longevity Risk and Capital Markets Solutions Conference," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 84(S1), pages 515-532, April.
    10. Blake, David & Cairns, Andrew J.G., 2021. "Longevity risk and capital markets: The 2019-20 update," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 395-439.
    11. Apicella, Giovanna & Dacorogna, Michel M, 2016. "A General framework for modelling mortality to better estimate its relationship with interest rate risks," MPRA Paper 75788, University Library of Munich, Germany.
    12. Jevtić, Petar & Regis, Luca, 2019. "A continuous-time stochastic model for the mortality surface of multiple populations," Insurance: Mathematics and Economics, Elsevier, vol. 88(C), pages 181-195.
    13. Boquan Cheng & Rogemar Mamon, 2023. "A uniformisation-driven algorithm for inference-related estimation of a phase-type ageing model," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 29(1), pages 142-187, January.
    14. Hainaut, Donatien & Devolder, Pierre & Pelsser, Antoon, 2018. "Robust evaluation of SCR for participating life insurances under Solvency II," Insurance: Mathematics and Economics, Elsevier, vol. 79(C), pages 107-123.
    15. Gao, Quansheng & He, Ting & Zhang, Chi, 2011. "Quantile hedging for equity-linked life insurance contracts in a stochastic interest rate economy," Economic Modelling, Elsevier, vol. 28(1), pages 147-156.
    16. Zhao, Yixing & Mamon, Rogemar, 2018. "An efficient algorithm for the valuation of a guaranteed annuity option with correlated financial and mortality risks," Insurance: Mathematics and Economics, Elsevier, vol. 78(C), pages 1-12.
    17. Meyricke, Ramona & Sherris, Michael, 2013. "The determinants of mortality heterogeneity and implications for pricing annuities," Insurance: Mathematics and Economics, Elsevier, vol. 53(2), pages 379-387.
    18. Ankush Agarwal & Christian-Oliver Ewald & Yongjie Wang, 2023. "Hedging longevity risk in defined contribution pension schemes," Computational Management Science, Springer, vol. 20(1), pages 1-34, December.
    19. Eckhard Platen, 2009. "Real World Pricing of Long Term Contracts," Research Paper Series 262, Quantitative Finance Research Centre, University of Technology, Sydney.
    20. Cupido, Kyran & Jevtić, Petar & Paez, Antonio, 2020. "Spatial patterns of mortality in the United States: A spatial filtering approach," Insurance: Mathematics and Economics, Elsevier, vol. 95(C), pages 28-38.

    More about this item

    Keywords

    Pensions; Insurance; Retirement; Longevity risk; Biological age;
    All these keywords.

    JEL classification:

    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

    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:92:y:2020:i:c:p:147-161. 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.