IDEAS home Printed from https://ideas.repec.org/a/eee/insuma/v72y2017icp175-188.html
   My bibliography  Save this article

Redistribution of longevity risk: The effect of heterogeneous mortality beliefs

Author

Listed:
  • Boonen, Tim J.
  • De Waegenaere, Anja
  • Norde, Henk

Abstract

Existing literature regarding the natural hedge potential that arises from combining different longevity-linked liabilities typically does not address the question how changes in the liability mix can be obtained. We consider firms who aim to exploit the benefits of natural hedge potential by redistributing their risks, and characterize the risk redistributions that will arise when the parties bargain for a redistribution of risk that weakly benefits them all. We analyze the effects of heterogeneity in the beliefs regarding the probability distribution of future mortality rates on the properties of these risk redistributions, and provide a numerical illustration for a case where an insurer with a portfolio of term assurance contracts and a pension fund with a portfolio of life annuities redistribute their risks.

Suggested Citation

  • Boonen, Tim J. & De Waegenaere, Anja & Norde, Henk, 2017. "Redistribution of longevity risk: The effect of heterogeneous mortality beliefs," Insurance: Mathematics and Economics, Elsevier, vol. 72(C), pages 175-188.
    • Handle: RePEc:eee:insuma:v:72:y:2017:i:c:p:175-188
    DOI: 10.1016/j.insmatheco.2016.11.004
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167668716302827
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.insmatheco.2016.11.004?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. Rubinstein, Ariel, 1982. "Perfect Equilibrium in a Bargaining Model," Econometrica, Econometric Society, vol. 50(1), pages 97-109, January.
    2. Cairns, Andrew J.G. & Blake, David & Dowd, Kevin & Coughlan, Guy D. & Epstein, David & Khalaf-Allah, Marwa, 2011. "Mortality density forecasts: An analysis of six stochastic mortality models," Insurance: Mathematics and Economics, Elsevier, vol. 48(3), pages 355-367, May.
    3. Koissi, Marie-Claire & Shapiro, Arnold F. & Hognas, Goran, 2006. "Evaluating and extending the Lee-Carter model for mortality forecasting: Bootstrap confidence interval," Insurance: Mathematics and Economics, Elsevier, vol. 38(1), pages 1-20, February.
    4. van Gulick, Gerwald & De Waegenaere, Anja & Norde, Henk, 2012. "Excess based allocation of risk capital," Insurance: Mathematics and Economics, Elsevier, vol. 50(1), pages 26-42.
    5. Richards, S. J. & Currie, I. D. & Ritchie, G. P., 2014. "A Value-at-Risk framework for longevity trend risk," British Actuarial Journal, Cambridge University Press, vol. 19(1), pages 116-139, March.
    6. Boonen, Tim J., 2016. "Nash equilibria of Over-The-Counter bargaining for insurance risk redistributions: The role of a regulator," European Journal of Operational Research, Elsevier, vol. 250(3), pages 955-965.
    7. Richards, Stephen, 2014. "A Value-at-Risk framework for longevity trend risk ‐ Abstract of the London discussion," British Actuarial Journal, Cambridge University Press, vol. 19(1), pages 157-167, March.
    8. Plat, Richard, 2009. "On stochastic mortality modeling," Insurance: Mathematics and Economics, Elsevier, vol. 45(3), pages 393-404, December.
    9. 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.
    10. Haberman, Steven & Renshaw, Arthur, 2012. "Parametric mortality improvement rate modelling and projecting," Insurance: Mathematics and Economics, Elsevier, vol. 50(3), pages 309-333.
    11. Blake, D. & Cairns, A. J. G. & Dowd, K., 2006. "Living with Mortality: Longevity Bonds and Other Mortality-Linked Securities," British Actuarial Journal, Cambridge University Press, vol. 12(1), pages 153-197, March.
    12. Olivier Compte & Philippe Jehiel, 2010. "The Coalitional Nash Bargaining Solution," Econometrica, Econometric Society, vol. 78(5), pages 1593-1623, September.
    13. Damme, Eric van, 1986. "The Nash bargaining solution is optimal," Journal of Economic Theory, Elsevier, vol. 38(1), pages 78-100, February.
    14. Li, Jackie & Haberman, Steven, 2015. "On the effectiveness of natural hedging for insurance companies and pension plans," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 286-297.
    15. Schlesinger, Harris, 1984. "Two-person insurance negotiation," Insurance: Mathematics and Economics, Elsevier, vol. 3(3), pages 147-149, July.
    16. Pitacco, Ermanno & Denuit, Michel & Haberman, Steven & Olivieri, Annamaria, 2009. "Modelling Longevity Dynamics for Pensions and Annuity Business," OUP Catalogue, Oxford University Press, number 9780199547272.
    17. Börger, Matthias & Fleischer, Daniel & Kuksin, Nikita, 2014. "Modeling The Mortality Trend Under Modern Solvency Regimes," ASTIN Bulletin, Cambridge University Press, vol. 44(1), pages 1-38, January.
    18. Haberman, Steven & Renshaw, Arthur, 2011. "A comparative study of parametric mortality projection models," Insurance: Mathematics and Economics, Elsevier, vol. 48(1), pages 35-55, January.
    19. Riddell, W Craig, 1981. "Bargaining under Uncertainty," American Economic Review, American Economic Association, vol. 71(4), pages 579-590, September.
    20. Li, Hong & De Waegenaere, Anja & Melenberg, Bertrand, 2015. "The choice of sample size for mortality forecasting: A Bayesian learning approach," Insurance: Mathematics and Economics, Elsevier, vol. 63(C), pages 153-168.
    21. Ngai, Andrew & Sherris, Michael, 2011. "Longevity risk management for life and variable annuities: The effectiveness of static hedging using longevity bonds and derivatives," Insurance: Mathematics and Economics, Elsevier, vol. 49(1), pages 100-114, July.
    22. Geng Niu & Bertrand Melenberg, 2014. "Trends in Mortality Decrease and Economic Growth," Demography, Springer;Population Association of America (PAA), vol. 51(5), pages 1755-1773, October.
    23. John Quiggin & Robert G Chambers, 2009. "Bargaining Power and Efficiency in Insurance Contracts," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 34(1), pages 47-73, June.
    24. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    25. Richards, Stephen, 2014. "A Value-at-Risk framework for longevity trend risk ‐ Abstract of the Edinburgh discussion," British Actuarial Journal, Cambridge University Press, vol. 19(1), pages 140-156, March.
    26. Acciaio, Beatrice & Svindland, Gregor, 2009. "Optimal risk sharing with different reference probabilities," LSE Research Online Documents on Economics 50119, London School of Economics and Political Science, LSE Library.
    27. Andrew J. G. Cairns & David Blake & Kevin Dowd, 2006. "A Two‐Factor Model for Stochastic Mortality with Parameter Uncertainty: Theory and Calibration," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 73(4), pages 687-718, December.
    28. Jennifer L. Wang & H.C. Huang & Sharon S. Yang & Jeffrey T. Tsai, 2010. "An Optimal Product Mix for Hedging Longevity Risk in Life Insurance Companies: The Immunization Theory Approach," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 77(2), pages 473-497, June.
    29. Plat, Richard, 2011. "One-year Value-at-Risk for longevity and mortality," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 462-470.
    30. Acciaio, Beatrice & Svindland, Gregor, 2009. "Optimal risk sharing with different reference probabilities," Insurance: Mathematics and Economics, Elsevier, vol. 44(3), pages 426-433, June.
    31. Hári, Norbert & De Waegenaere, Anja & Melenberg, Bertrand & Nijman, Theo E., 2008. "Longevity risk in portfolios of pension annuities," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 505-519, April.
    32. Dowd, Kevin & Cairns, Andrew J.G. & Blake, David & Coughlan, Guy D. & Epstein, David & Khalaf-Allah, Marwa, 2010. "Evaluating the goodness of fit of stochastic mortality models," Insurance: Mathematics and Economics, Elsevier, vol. 47(3), pages 255-265, December.
    33. Boonen, T.J., 2014. "Game-theoretic approaches to optimal risk sharing," Other publications TiSEM 5b1d2a57-dd10-437d-9f9b-6, Tilburg University, School of Economics and Management.
    34. Tsai, Jeffrey T. & Wang, Jennifer L. & Tzeng, Larry Y., 2010. "On the optimal product mix in life insurance companies using conditional value at risk," Insurance: Mathematics and Economics, Elsevier, vol. 46(1), pages 235-241, February.
    35. 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.
    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. Boonen, Tim J. & Jiang, Wenjun, 2022. "Bilateral risk sharing in a comonotone market with rank-dependent utilities," Insurance: Mathematics and Economics, Elsevier, vol. 107(C), pages 361-378.
    2. De-Lei Sheng & Linfeng Shi & Danping Li & Yanping Zhao, 2022. "Manage Pension Deficit with Heterogeneous Insurance," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 1119-1141, June.
    3. Cheung, Ka Chun & He, Wanting & Wang, He, 2023. "Multi-constrained optimal reinsurance model from the duality perspectives," Insurance: Mathematics and Economics, Elsevier, vol. 113(C), pages 199-214.
    4. Jiang, Wenjun & Ren, Jiandong & Yang, Chen & Hong, Hanping, 2019. "On optimal reinsurance treaties in cooperative game under heterogeneous beliefs," Insurance: Mathematics and Economics, Elsevier, vol. 85(C), pages 173-184.

    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. 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.
    2. 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.
    3. Boonen, T.J. & De Waegenaere, A.M.B. & Norde, H.W., 2012. "Bargaining for Over-The Counter Risk Redistributions : The Case of Longevity Risk," Discussion Paper 2012-090, Tilburg University, Center for Economic Research.
    4. Boonen, T.J. & De Waegenaere, A.M.B. & Norde, H.W., 2012. "Bargaining for Over-The Counter Risk Redistributions : The Case of Longevity Risk," Other publications TiSEM 666aa6f1-2d07-413c-90da-a, Tilburg University, School of Economics and Management.
    5. Boonen, Tim J., 2016. "Nash equilibria of Over-The-Counter bargaining for insurance risk redistributions: The role of a regulator," European Journal of Operational Research, Elsevier, vol. 250(3), pages 955-965.
    6. Hunt, Andrew & Blake, David, 2015. "Modelling longevity bonds: Analysing the Swiss Re Kortis bond," Insurance: Mathematics and Economics, Elsevier, vol. 63(C), pages 12-29.
    7. Börger, Matthias & Schupp, Johannes, 2018. "Modeling trend processes in parametric mortality models," Insurance: Mathematics and Economics, Elsevier, vol. 78(C), pages 369-380.
    8. Kallestrup-Lamb, Malene & Søgaard Laursen, Nicolai, 2024. "Longevity hedge effectiveness using socioeconomic indices," Insurance: Mathematics and Economics, Elsevier, vol. 114(C), pages 242-251.
    9. Liu, Yanxin & Li, Johnny Siu-Hang, 2016. "It’s all in the hidden states: A longevity hedging strategy with an explicit measure of population basis risk," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 301-319.
    10. David Blake & Andrew Cairns & Guy Coughlan & Kevin Dowd & Richard MacMinn, 2013. "The New Life Market," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 80(3), pages 501-558, September.
    11. Colin O’hare & Youwei Li, 2017. "Modelling mortality: are we heading in the right direction?," Applied Economics, Taylor & Francis Journals, vol. 49(2), pages 170-187, January.
    12. Broeders, Dirk & Mehlkopf, Roel & van Ool, Annick, 2021. "The economics of sharing macro-longevity risk," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 440-458.
    13. Jaap Spreeuw & Iqbal Owadally & Muhammad Kashif, 2022. "Projecting Mortality Rates Using a Markov Chain," Mathematics, MDPI, vol. 10(7), pages 1-18, April.
    14. Anja De Waegenaere & Bertrand Melenberg & Ralph Stevens, 2010. "Longevity Risk," De Economist, Springer, vol. 158(2), pages 151-192, June.
    15. Lin, Tzuling & Wang, Chou-Wen & Tsai, Cary Chi-Liang, 2015. "Age-specific copula-AR-GARCH mortality models," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 110-124.
    16. Katrien Antonio & Anastasios Bardoutsos & Wilbert Ouburg, 2015. "Bayesian Poisson log-bilinear models for mortality projections with multiple populations," Working Papers Department of Accountancy, Finance and Insurance (AFI), Leuven 485564, KU Leuven, Faculty of Economics and Business (FEB), Department of Accountancy, Finance and Insurance (AFI), Leuven.
    17. 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.
    18. Basellini, Ugofilippo & Camarda, Carlo Giovanni & Booth, Heather, 2023. "Thirty years on: A review of the Lee–Carter method for forecasting mortality," International Journal of Forecasting, Elsevier, vol. 39(3), pages 1033-1049.
    19. Man Chung Fung & Gareth W. Peters & Pavel V. Shevchenko, 2016. "A unified approach to mortality modelling using state-space framework: characterisation, identification, estimation and forecasting," Papers 1605.09484, arXiv.org.
    20. Helena Chuliá & Montserrat Guillén & Jorge M. Uribe, 2015. "Mortality and Longevity Risks in the United Kingdom: Dynamic Factor Models and Copula-Functions," Working Papers 2015-03, Universitat de Barcelona, UB Riskcenter.

    More about this item

    Keywords

    Risk redistribution; Longevity risk; Nash bargaining; Heterogeneous beliefs; Natural hedge potential;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies
    • J11 - Labor and Demographic Economics - - Demographic Economics - - - Demographic Trends, Macroeconomic Effects, and Forecasts

    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:72:y:2017:i:c:p:175-188. 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.