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Entropy, longevity and the cost of annuities

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  • Haberman, Steven
  • Khalaf-Allah, Marwa
  • Verrall, Richard

Abstract

This paper presents an extension of the application of the concept of entropy to annuity costs. Keyfitz (1985) introduced the concept of entropy, and analysed this in the context of continuous changes in life expectancy. He showed that a higher level of entropy indicates that the life expectancy has a greater propensity to respond to a change in the force of mortality than a lower level of entropy. In other words, a high level of entropy means that further reductions in mortality rates would have an impact on measures like life expectancy. In this paper, we apply this to the cost of annuities and show how it allows the sensitivity of the cost of a life annuity contract to changes in longevity to be summarized in a single figure index.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:insuma:v:48:y:2011:i:2:p:197-204
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    References listed on IDEAS

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    1. Sithole, Terry Z. & Haberman, Steven & Verrall, Richard J., 2000. "An investigation into parametric models for mortality projections, with applications to immediate annuitants' and life office pensioners' data," Insurance: Mathematics and Economics, Elsevier, vol. 27(3), pages 285-312, December.
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    4. Pitacco, Ermanno & Denuit, Michel & Haberman, Steven & Olivieri, Annamaria, 2009. "Modelling Longevity Dynamics for Pensions and Annuity Business," OUP Catalogue, Oxford University Press, number 9780199547272.
    5. Khalaf-Allah, M. & Haberman, S. & Verrall, R., 2006. "Measuring the effect of mortality improvements on the cost of annuities," Insurance: Mathematics and Economics, Elsevier, vol. 39(2), pages 231-249, October.
    6. Eduardo Arriaga, 1984. "Measuring and explaining the change in life expectancies," Demography, Springer;Population Association of America (PAA), vol. 21(1), pages 83-96, February.
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    Cited by:

    1. Rabitti, Giovanni & Borgonovo, Emanuele, 2020. "Is mortality or interest rate the most important risk in annuity models? A comparison of sensitivity analysis methods," Insurance: Mathematics and Economics, Elsevier, vol. 95(C), pages 48-58.
    2. Andrea Nigri & Elisabetta Barbi & Susanna Levantesi, 2022. "The relationship between longevity and lifespan variation," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 31(3), pages 481-493, September.
    3. 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.
    4. Psarrakos, Georgios & Toomaj, Abdolsaeed & Vliora, Polyxeni, 2024. "A family of variability measures based on the cumulative residual entropy and distortion functions," Insurance: Mathematics and Economics, Elsevier, vol. 114(C), pages 212-222.
    5. 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.
    6. Baishuai Zuo & Chuancun Yin, 2024. "Worst-cases of distortion riskmetrics and weighted entropy with partial information," Papers 2405.19075, arXiv.org.
    7. Psarrakos, Georgios & Vliora, Polyxeni, 2021. "Sensitivity analysis and tail variability for the Wang’s actuarial index," Insurance: Mathematics and Economics, Elsevier, vol. 98(C), pages 147-152.
    8. Gomes-Gonçalves, Erika & Gzyl, Henryk & Mayoral, Silvia, 2015. "Two maxentropic approaches to determine the probability density of compound risk losses," Insurance: Mathematics and Economics, Elsevier, vol. 62(C), pages 42-53.
    9. 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.
    10. Psarrakos, Georgios & Sordo, Miguel A., 2019. "On a family of risk measures based on proportional hazards models and tail probabilities," Insurance: Mathematics and Economics, Elsevier, vol. 86(C), pages 232-240.
    11. Amancio Betzuen Zalbidegoitia & Amaia Jone Betzuen Álvarez, 2021. "Is Longevity Acceleration Sustainable? An Entropy-Based Trial of the Population of Spain vs. Japan," Mathematics, MDPI, vol. 9(15), pages 1-18, July.

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