IDEAS home Printed from https://ideas.repec.org/a/eee/insuma/v48y2011i2p197-204.html
   My bibliography  Save this article

Entropy, longevity and the cost of annuities

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-6687(10)00111-3
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. J. Pollard, 1988. "On the decomposition of changes in expectation of life and differentials in life expectancy," Demography, Springer;Population Association of America (PAA), vol. 25(2), pages 265-276, May.
    2. 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.
    3. 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.
    4. 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.
    5. Noreen Goldman & Graham Lord, 1986. "A new look at entropy and the life table," Demography, Springer;Population Association of America (PAA), vol. 23(2), pages 275-282, May.
    6. Pitacco, Ermanno & Denuit, Michel & Haberman, Steven & Olivieri, Annamaria, 2009. "Modelling Longevity Dynamics for Pensions and Annuity Business," OUP Catalogue, Oxford University Press, number 9780199547272.
    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. 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.
    2. 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.
    3. 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.
    4. 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.
    5. Zuo, Baishuai & Yin, Chuancun, 2025. "Worst-case distortion riskmetrics and weighted entropy with partial information," European Journal of Operational Research, Elsevier, vol. 321(2), pages 476-492.
    6. 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.
    7. Baishuai Zuo & Chuancun Yin, 2025. "Analyzing distortion riskmetrics and weighted entropy for unimodal and symmetric distributions under partial information constraints," Papers 2504.19725, arXiv.org.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. Baishuai Zuo & Chuancun Yin, 2024. "Worst-cases of distortion riskmetrics and weighted entropy with partial information," Papers 2405.19075, arXiv.org.

    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. José Manuel Aburto & James W. Vaupel & Jesús-Adrián Alvarez & Francisco Villavicencio, 2019. "The threshold age of the lifetable entropy," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 41(4), pages 83-102.
    2. Marcia de Castro, 2001. "Changes in mortality and life expectancy: Some methodological issues," Mathematical Population Studies, Taylor & Francis Journals, vol. 9(3-4), pages 181-208.
    3. 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.
    4. Henrik Brønnum-Hansen & Juan Carlos Albizu-Campos Espiñeira & Camila Perera & Ingelise Andersen, 2023. "Trends in mortality patterns in two countries with different welfare models: comparisons between Cuba and Denmark 1955–2020," Journal of Population Research, Springer, vol. 40(2), pages 1-28, June.
    5. Karina Acosta-Ordoñez & Julio E. Romero-Prieto, 2017. "Cambios recientes en las principales causas de mortalidad en Colombia," Chapters, in: Jaime Bonet & Karelys Guzmán-Finol & Lucas Wilfried Hahn-De-Castro (ed.), La salud en Colombia: una perspectiva regional, chapter 4, pages 79-119, Banco de la Republica de Colombia.
    6. Branislav Šprocha & Branislav Bleha, 2021. "Mortality, Health Status and Self-Perception of Health in Slovak Roma Communities," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 153(3), pages 1065-1086, February.
    7. Evgeny M. Andreev & Vladimir M. Shkolnikov & Alexander Z. Begun, 2002. "Algorithm for decomposition of differences between aggregate demographic measures and its application to life expectancies, Gini coefficients, health expectancies, parity-progression ratios and total ," MPIDR Working Papers WP-2002-035, Max Planck Institute for Demographic Research, Rostock, Germany.
    8. Beltrán-Sánchez, Hiram & Soneji, Samir, 2011. "A unifying framework for assessing changes in life expectancy associated with changes in mortality: The case of violent deaths," Theoretical Population Biology, Elsevier, vol. 80(1), pages 38-48.
    9. Hatzopoulos, P. & Haberman, S., 2011. "A dynamic parameterization modeling for the age-period-cohort mortality," Insurance: Mathematics and Economics, Elsevier, vol. 49(2), pages 155-174, September.
    10. Margaret M. Weden, 2007. "Twentieth Century U.S. Racial Inequalities in Mortality Changes in the Average Age of Death and the Variability in the Age of Death for White and non-White Men and Women, 1900-2002," Working Papers WR-497, RAND Corporation.
    11. Per Kragh Andersen & Vladimir Canudas-Romo & Niels Keiding, 2013. "Cause-specific measures of life years lost," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 29(41), pages 1127-1152.
    12. Peng Fei & Philippe Wanner & Stephane Cotter, 1997. "Approche dynamique de la différence d'espérance de vie entre hommes et femmes en Suisse, entre 1910/11 et 1988/93. Une application des méthodes de décomposition de POLLARD et D'ARRIAGA," Swiss Journal of Economics and Statistics (SJES), Swiss Society of Economics and Statistics (SSES), vol. 133(IV), pages 741-754, December.
    13. Audrey Ugarte & Onofre Alves Simões, 2020. "Breaking Life Expectancy into Small Pieces," Working Papers REM 2020/0154, ISEG - Lisbon School of Economics and Management, REM, Universidade de Lisboa.
    14. Alyson Raalte & Hal Caswell, 2013. "Perturbation Analysis of Indices of Lifespan Variability," Demography, Springer;Population Association of America (PAA), vol. 50(5), pages 1615-1640, October.
    15. Udaya Mishra, 2006. "Making Comparisons of Demographic Aggregates more Meaningful: A Case of Life Expectancies and Total Fertility Rates," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 75(3), pages 445-461, February.
    16. Hatzopoulos, P. & Haberman, S., 2009. "A parameterized approach to modeling and forecasting mortality," Insurance: Mathematics and Economics, Elsevier, vol. 44(1), pages 103-123, February.
    17. Vladimir M. Shkolnikov & Evgeny M. Andreev & Alexander Z. Begun, 2001. "Gini coefficient as a life table function: computation from discrete data, decomposition of differences and empirical examples," MPIDR Working Papers WP-2001-017, Max Planck Institute for Demographic Research, Rostock, Germany.
    18. Hiram Beltran-Sanchez & Vladimir Canudas-Romo & Samuel Preston, 2008. "An integrated approach to cause-of-death analysis: cause-deleted life tables and decompositions of life expectancy," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 19(35), pages 1323-1350.
    19. James W. Vaupel & Vladimir Canudas Romo, 2002. "Decomposing change in life expectancy: a bouquet of formulas in honour of Nathan Keyfitz´s 90th birthday," MPIDR Working Papers WP-2002-042, Max Planck Institute for Demographic Research, Rostock, Germany.
    20. Goerlich, Francisco José & Pinilla, Rafael, 2005. "Esperanza de Vida y Potencial de Vida a lo largo del siglo XX en España [Live Expectancy and Potential throughout the twentieth century in Spain]," MPRA Paper 15911, University Library of Munich, Germany, revised 2005.

    More about this item

    Keywords

    ;

    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:48:y:2011:i:2:p:197-204. 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.