IDEAS home Printed from https://ideas.repec.org/a/eee/insuma/v119y2024icp146-156.html
   My bibliography  Save this article

Uniqueness of equilibrium with survival probability heterogeneity and endogenous annuity price

Author

Listed:
  • Lau, Sau-Him Paul
  • Ying, Yinan
  • Zhang, Qilin

Abstract

When annuitants' survival probabilities are heterogeneous, the equilibrium annuity price is affected by their annuitization choices, which further depend on the annuity price. Given this mutual dependence, it is generally difficult to establish uniqueness of the equilibrium. Based on similar expressions appearing in several annuity and insurance models, we obtain two results in an annuity model with heterogeneity in survival probability only. First, the equilibrium annuity price is always unique if the annuitization function is multiplicatively separable in survival probability and annuity price. Second, the equilibrium is unique for more general annuitization functions, provided that a sufficient condition on the distribution of survival probabilities holds. Many distributions, including the uniform, normal and gamma distributions, satisfy this condition.

Suggested Citation

  • Lau, Sau-Him Paul & Ying, Yinan & Zhang, Qilin, 2024. "Uniqueness of equilibrium with survival probability heterogeneity and endogenous annuity price," Insurance: Mathematics and Economics, Elsevier, vol. 119(C), pages 146-156.
    • Handle: RePEc:eee:insuma:v:119:y:2024:i:c:p:146-156
    DOI: 10.1016/j.insmatheco.2024.08.004
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167668724000945
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.insmatheco.2024.08.004?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

    for a different version of it.

    References listed on IDEAS

    as
    1. repec:spo:wpmain:info:hdl:2441/169d87l3e88rpoi5e1tgckfi6a is not listed on IDEAS
    2. Andrea Attar & Thomas Mariotti & François Salanié, 2011. "Nonexclusive Competition in the Market for Lemons," Econometrica, Econometric Society, vol. 79(6), pages 1869-1918, November.
    3. Abel, Andrew B, 1986. "Capital Accumulation and Uncertain Lifetimes with Adverse Selection," Econometrica, Econometric Society, vol. 54(5), pages 1079-1097, September.
    4. Jeffrey R. Brown, 2003. "Redistribution and Insurance: Mandatory Annuitization With Mortality Heterogeneity," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 70(1), pages 17-41, March.
    5. Steinorth, Petra, 2012. "The demand for enhanced annuities," Journal of Public Economics, Elsevier, vol. 96(11), pages 973-980.
    6. Sau‐Him Paul Lau & Qilin Zhang, 2023. "A common thread linking the design of guarantee and nonescalating payments of public annuities," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 90(3), pages 703-742, September.
    7. Nicolas Coeurdacier & Stéphane Guibaud & Keyu Jin, 2015. "Credit Constraints and Growth in a Global Economy," American Economic Review, American Economic Association, vol. 105(9), pages 2838-2881, September.
    8. Robert J. Barro & Robert G. King, 1984. "Time-Separable Preferences and Intertemporal-Substitution Models of Business Cycles," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 99(4), pages 817-839.
    9. repec:dau:papers:123456789/5363 is not listed on IDEAS
    10. Alai, Daniel H. & Landsman, Zinoviy & Sherris, Michael, 2013. "Lifetime dependence modelling using a truncated multivariate gamma distribution," Insurance: Mathematics and Economics, Elsevier, vol. 52(3), pages 542-549.
    11. Shlomo Benartzi & Alessandro Previtero & Richard H. Thaler, 2011. "Annuitization Puzzles," Journal of Economic Perspectives, American Economic Association, vol. 25(4), pages 143-164, Fall.
    12. Tomas Philipson & John Cawley, 1999. "An Empirical Examination of Information Barriers to Trade in Insurance," American Economic Review, American Economic Association, vol. 89(4), pages 827-846, September.
    13. Eichenbaum, Martin S & Peled, Dan, 1987. "Capital Accumulation and Annuities in an Adverse Selection Economy," Journal of Political Economy, University of Chicago Press, vol. 95(2), pages 334-354, April.
    14. Li, Johnny Siu-Hang & Hardy, Mary R. & Tan, Ken Seng, 2009. "Uncertainty in Mortality Forecasting: An Extension to the Classical Lee-Carter Approach," ASTIN Bulletin, Cambridge University Press, vol. 39(1), pages 137-164, May.
    15. Hanming Fang & Michael P. Keane & Dan Silverman, 2008. "Sources of Advantageous Selection: Evidence from the Medigap Insurance Market," Journal of Political Economy, University of Chicago Press, vol. 116(2), pages 303-350, April.
    16. Thomas Davidoff & Jeffrey R. Brown & Peter A. Diamond, 2005. "Annuities and Individual Welfare," American Economic Review, American Economic Association, vol. 95(5), pages 1573-1590, December.
    17. Roozbeh Hosseini, 2015. "Adverse Selection in the Annuity Market and the Role for Social Security," Journal of Political Economy, University of Chicago Press, vol. 123(4), pages 941-984.
    18. Menahem E. Yaari, 1965. "Uncertain Lifetime, Life Insurance, and the Theory of the Consumer," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 32(2), pages 137-150.
    19. Ilona Babenko & Oliver Boguth & Yuri Tserlukevich, 2016. "Idiosyncratic Cash Flows and Systematic Risk," Journal of Finance, American Finance Association, vol. 71(1), pages 425-456, February.
    20. Brugiavini, Agar, 1993. "Uncertainty resolution and the timing of annuity purchases," Journal of Public Economics, Elsevier, vol. 50(1), pages 31-62, January.
    21. repec:hal:spmain:info:hdl:2441/169d87l3e88rpoi5e1tgckfi6a is not listed on IDEAS
    22. Bertrand Villeneuve, 2003. "Mandatory Pensions and the Intensity of Adverse Selection in Life Insurance Markets," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 70(3), pages 527-548, September.
    23. Wen, Jie & Cairns, Andrew J.G. & Kleinow, Torsten, 2023. "Modelling socio-economic mortality at neighbourhood level," ASTIN Bulletin, Cambridge University Press, vol. 53(2), pages 285-310, May.
    24. Bella Vakulenko‐Lagun & Micha Mandel & Rebecca A. Betensky, 2020. "Inverse probability weighting methods for Cox regression with right‐truncated data," Biometrics, The International Biometric Society, vol. 76(2), pages 484-495, June.
    25. Nicolas Coeurdacier & Stéphane Guibaud & Keyu Jin, 2015. "Credit Constraints and Growth in a Global Economy," SciencePo Working papers hal-03392968, HAL.
    26. Lee Lockwood, 2012. "Bequest Motives and the Annuity Puzzle," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 15(2), pages 226-243, April.
    27. Fangfang Bai & Xuerong Chen & Yan Chen & Tao Huang, 2019. "A general quantile residual life model for length‐biased right‐censored data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 46(4), pages 1191-1205, December.
    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. Lau, Sau-Him Paul & Ying, Yinan, 2024. "Deferred annuities with gender-neutral pricing: Benefitting most women without adversely affecting too many men," Journal of Economic Dynamics and Control, Elsevier, vol. 168(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. Sau‐Him Paul Lau & Qilin Zhang, 2023. "A common thread linking the design of guarantee and nonescalating payments of public annuities," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 90(3), pages 703-742, September.
    2. Fang, H., 2016. "Insurance Markets for the Elderly," Handbook of the Economics of Population Aging, in: Piggott, John & Woodland, Alan (ed.), Handbook of the Economics of Population Aging, edition 1, volume 1, chapter 0, pages 237-309, Elsevier.
    3. Oded Palmon & Avia Spivak, 2007. "Adverse selection and the market for annuities," The Geneva Papers on Risk and Insurance Theory, Springer;International Association for the Study of Insurance Economics (The Geneva Association), vol. 32(1), pages 37-59, June.
    4. Steinorth, Petra, 2012. "The demand for enhanced annuities," Journal of Public Economics, Elsevier, vol. 96(11), pages 973-980.
    5. Kaschützke, B. & Maurer, R., 2016. "Investing and Portfolio Allocation for Retirement," Handbook of the Economics of Population Aging, in: Piggott, John & Woodland, Alan (ed.), Handbook of the Economics of Population Aging, edition 1, volume 1, chapter 0, pages 567-608, Elsevier.
    6. Erin Cottle Hunt & Frank N. Caliendo, 2022. "Social security and risk sharing: A survey of four decades of economic analysis," Journal of Economic Surveys, Wiley Blackwell, vol. 36(5), pages 1591-1609, December.
    7. Horneff, Vanya & Kaschützke, Barbara & Maurer, Raimond & Rogalla, Ralph, 2014. "Welfare implications of product choice regulation during the payout phase of funded pensions," Journal of Pension Economics and Finance, Cambridge University Press, vol. 13(3), pages 272-296, July.
    8. repec:dau:papers:123456789/5369 is not listed on IDEAS
    9. Maria Alexandrova & Nadine Gatzert, 2019. "What Do We Know About Annuitization Decisions?," Risk Management and Insurance Review, American Risk and Insurance Association, vol. 22(1), pages 57-100, March.
    10. d’Albis, Hippolyte & Kalk, Andrei, 2021. "Why do we postpone annuity purchases?," Journal of Mathematical Economics, Elsevier, vol. 95(C).
    11. Torben M. Andersen, 2024. "Hedging mortality risk over the life‐cycle—The role of information and borrowing constraints," Economic Inquiry, Western Economic Association International, vol. 62(4), pages 1449-1466, October.
    12. Hippolyte d'Albis & Johanna Etner, 2018. "Illiquid life annuities," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 20(2), pages 277-297, April.
    13. Lau, Sau-Him Paul & Ying, Yinan, 2024. "Deferred annuities with gender-neutral pricing: Benefitting most women without adversely affecting too many men," Journal of Economic Dynamics and Control, Elsevier, vol. 168(C).
    14. M. Martin Boyer & Franca Glenzer, 2021. "Pensions, annuities, and long-term care insurance: on the impact of risk screening," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 46(2), pages 133-174, September.
    15. Andrea Attar & Thomas Mariotti & François Salanié, 2021. "Entry-Proofness and Discriminatory Pricing under Adverse Selection," American Economic Review, American Economic Association, vol. 111(8), pages 2623-2659, August.
    16. Wang, Ting & Young, Virginia R., 2012. "Maximizing the utility of consumption with commutable life annuities," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 352-369.
    17. Cormac O'Dea & David Sturrock, 2023. "Survival Pessimism and the Demand for Annuities," The Review of Economics and Statistics, MIT Press, vol. 105(2), pages 442-457, March.
    18. Johannes Hagen, 2015. "The determinants of annuitization: evidence from Sweden," International Tax and Public Finance, Springer;International Institute of Public Finance, vol. 22(4), pages 549-578, August.
    19. Hippolyte d’Albis & Emmanuel Thibault, 2018. "Ambiguous life expectancy and the demand for annuities," Theory and Decision, Springer, vol. 85(3), pages 303-319, October.
    20. Hanming Fang & Michael P. Keane & Dan Silverman, 2008. "Sources of Advantageous Selection: Evidence from the Medigap Insurance Market," Journal of Political Economy, University of Chicago Press, vol. 116(2), pages 303-350, April.
    21. Amy Finkelstein & James Poterba, 2002. "Selection Effects in the United Kingdom Individual Annuities Market," Economic Journal, Royal Economic Society, vol. 112(476), pages 28-50, January.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    JEL classification:

    • D15 - Microeconomics - - Household Behavior - - - Intertemporal Household Choice; Life Cycle Models and Saving
    • G52 - Financial Economics - - Household Finance - - - Insurance

    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:119:y:2024:i:c:p:146-156. 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.