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Actuarial fairness and social welfare in mixed-cohort tontines

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  • Chen, An
  • Rach, Manuel

Abstract

We study actuarial fairness in tontines with heterogeneous cohorts. For a given tontine, we show that both collective and individual actuarial fairness can be achieved. While it is impossible to design a tontine scheme with mixed cohorts that is optimal (utility-maximizing) for each single cohort (Milevsky and Salisbury (2016), Chen et al. (2021d)), we design a socially optimal tontine that maximizes the collective's expected utility which is characterized through a weighted sum of individual utility functions. In particular, we compare the resulting collectively optimal tontine to existing schemes in the literature, and identify similarities and differences as well as potential (dis-)advantages.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:insuma:v:111:y:2023:i:c:p:214-229
    DOI: 10.1016/j.insmatheco.2023.05.002
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    1. Amadeu DaSilva & Mira Farka & Christos Giannikos, 2019. "Age‐Dependent Increasing Risk Aversion and the Equity Premium Puzzle," The Financial Review, Eastern Finance Association, vol. 54(2), pages 377-412, May.
    2. Milevsky, Moshe A. & Salisbury, Thomas S., 2016. "Equitable Retirement Income Tontines: Mixing Cohorts Without Discriminating," ASTIN Bulletin, Cambridge University Press, vol. 46(3), pages 571-604, September.
    3. Chen, An & Nguyen, Thai & Rach, Manuel, 2021. "Optimal collective investment: The impact of sharing rules, management fees and guarantees," Journal of Banking & Finance, Elsevier, vol. 123(C).
    4. Amershi, Amin H & Stoeckenius, Jan H W, 1983. "The Theory of Syndicates and Linear Sharing Rules," Econometrica, Econometric Society, vol. 51(5), pages 1407-1416, September.
    5. Schumacher, Johannes M., 2018. "Linear Versus Nonlinear Allocation Rules In Risk Sharing Under Financial Fairness," ASTIN Bulletin, Cambridge University Press, vol. 48(3), pages 995-1024, September.
    6. Huang, Chi-fu & Litzenberger, Robert, 1985. "On the Necessary Condition for Linear Sharing and Separation: A Note," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 20(3), pages 381-384, September.
    7. Milevsky, Moshe A. & Salisbury, Thomas S., 2015. "Optimal retirement income tontines," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 91-105.
    8. Pazdera, Jaroslav & Schumacher, Johannes M. & Werker, Bas J.M., 2016. "Cooperative investment in incomplete markets under financial fairness," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 394-406.
    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. Hieber, Peter & Lucas, Nathalie, 2022. "Modern Life-Care Tontines," ASTIN Bulletin, Cambridge University Press, vol. 52(2), pages 563-589, May.
    11. 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.
    12. Stamos, Michael Z., 2008. "Optimal consumption and portfolio choice for pooled annuity funds," Insurance: Mathematics and Economics, Elsevier, vol. 43(1), pages 56-68, August.
    13. An Chen & Thai Nguyen & Manuel Rach, 2021. "A collective investment problem in a stochastic volatility environment: The impact of sharing rules," Annals of Operations Research, Springer, vol. 302(1), pages 85-109, July.
    14. Dumas, Bernard, 1989. "Two-Person Dynamic Equilibrium in the Capital Market," The Review of Financial Studies, Society for Financial Studies, vol. 2(2), pages 157-188.
    15. An Chen & Linyi Qian & Zhixin Yang, 2021. "Tontines with mixed cohorts," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2021(5), pages 437-455, May.
    16. Chen, An & Chen, Yusha & Xu, Xian, 2022. "Care-dependent tontines," Insurance: Mathematics and Economics, Elsevier, vol. 106(C), pages 69-89.
    17. Yijia Lin & Samuel H. Cox, 2005. "Securitization of Mortality Risks in Life Annuities," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 72(2), pages 227-252, June.
    18. John Piggott & Emiliano A. Valdez & Bettina Detzel, 2005. "The Simple Analytics of a Pooled Annuity Fund," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 72(3), pages 497-520, September.
    19. Hanewald, Katja & Piggott, John & Sherris, Michael, 2013. "Individual post-retirement longevity risk management under systematic mortality risk," Insurance: Mathematics and Economics, Elsevier, vol. 52(1), pages 87-97.
    20. 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.
    21. Bjarne Astrup Jensen & Jørgen Aase Nielsen, 2016. "How suboptimal are linear sharing rules?," Annals of Finance, Springer, vol. 12(2), pages 221-243, May.
    22. Denuit, Michel, 2019. "Size-Biased Transform And Conditional Mean Risk Sharing, With Application To P2p Insurance And Tontines," ASTIN Bulletin, Cambridge University Press, vol. 49(3), pages 591-617, September.
    23. Chao Qiao & Michael Sherris, 2013. "Managing Systematic Mortality Risk With Group Self-Pooling and Annuitization Schemes," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 80(4), pages 949-974, December.
    24. Chen, An & Hieber, Peter & Klein, Jakob K., 2019. "Tonuity: A Novel Individual-Oriented Retirement Plan," ASTIN Bulletin, Cambridge University Press, vol. 49(1), pages 5-30, January.
    25. Chen, An & Rach, Manuel & Sehner, Thorsten, 2020. "On The Optimal Combination Of Annuities And Tontines," ASTIN Bulletin, Cambridge University Press, vol. 50(1), pages 95-129, January.
    26. Donnelly, Catherine, 2015. "Actuarial Fairness And Solidarity In Pooled Annuity Funds," ASTIN Bulletin, Cambridge University Press, vol. 45(1), pages 49-74, January.
    27. Denuit, Michel, 2019. "Size-biased transform and conditional mean risk sharing, with application to P2P insurance and tontines," LIDAM Discussion Papers ISBA 2019010, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    28. Denuit, Michel, 2019. "Size-biased transform and conditional mean risk sharing, with application to P2P insurance and tontines," LIDAM Reprints ISBA 2019038, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    29. Weinbaum, David, 2009. "Investor heterogeneity, asset pricing and volatility dynamics," Journal of Economic Dynamics and Control, Elsevier, vol. 33(7), pages 1379-1397, July.
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    More about this item

    Keywords

    Tontine; Actuarial fairness; Participation rates; Age heterogeneity; Risk aversion;
    All these keywords.

    JEL classification:

    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies
    • G52 - Financial Economics - - Household Finance - - - Insurance
    • H31 - Public Economics - - Fiscal Policies and Behavior of Economic Agents - - - Household
    • J32 - Labor and Demographic Economics - - Wages, Compensation, and Labor Costs - - - Nonwage Labor Costs and Benefits; Retirement Plans; Private Pensions

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