IDEAS home Printed from https://ideas.repec.org/a/eee/insuma/v125y2025ics0167668725001088.html

Individual survivor fund account: The impact of bequest motives on tontine participation

Author

Listed:
  • Ng, Tak Wa
  • Nguyen, Thai

Abstract

We introduce a new model for individual survivor fund account with bequest that allows the tontine's participants to leave inheritances to their heirs. Two proposed designs, constant and variable participation, are examined through the lens of an individual account, addressing optimal investment and bequest proportions. Our formulation captures two types of bequest motives: the relative concern between terminal benefit and premature bequest and the intention to smooth the bequest plan. Our numerical illustrations show that the individual's willingness to participate in the longevity risk pool will decrease with these two bequest motive levels and address the question of when and with what motive level the individual will join the pool. Furthermore, we incorporate labor income and consumption in the participant's optimization problem and perform a welfare analysis thereon.

Suggested Citation

  • Ng, Tak Wa & Nguyen, Thai, 2025. "Individual survivor fund account: The impact of bequest motives on tontine participation," Insurance: Mathematics and Economics, Elsevier, vol. 125(C).
    • Handle: RePEc:eee:insuma:v:125:y:2025:i:c:s0167668725001088
    DOI: 10.1016/j.insmatheco.2025.103161
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167668725001088
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.insmatheco.2025.103161?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. Marcel Bräutigam & Montserrat Guillén & Jens P. Nielsen, 2017. "Facing Up to Longevity with Old Actuarial Methods: A Comparison of Pooled Funds and Income Tontines," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 42(3), pages 406-422, July.
    2. 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.
    3. Dhaene, Jan & Milevsky, Moshe A., 2024. "Egalitarian pooling and sharing of longevity risk a.k.a. can an administrator help skin the tontine cat?," Insurance: Mathematics and Economics, Elsevier, vol. 119(C), pages 238-250.
    4. Valdez, Emiliano A. & Piggott, John & Wang, Liang, 2006. "Demand and adverse selection in a pooled annuity fund," Insurance: Mathematics and Economics, Elsevier, vol. 39(2), pages 251-266, October.
    5. Donnelly, C. & Young, J., 2017. "Product options for enhanced retirement income," British Actuarial Journal, Cambridge University Press, vol. 22(3), pages 636-656, September.
    6. Denuit, Michel & Dhaene, Jan, 2012. "Convex order and comonotonic conditional mean risk sharing," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 265-270.
    7. Blanchet-Scalliet, Christophette & El Karoui, Nicole & Jeanblanc, Monique & Martellini, Lionel, 2008. "Optimal investment decisions when time-horizon is uncertain," Journal of Mathematical Economics, Elsevier, vol. 44(11), pages 1100-1113, December.
    8. An Chen & Thai Nguyen & Thorsten Sehner, 2022. "Unit-Linked Tontine: Utility-Based Design, Pricing and Performance," Risks, MDPI, vol. 10(4), pages 1-27, April.
    9. 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.
    10. Morten Tolver Kronborg & Mogens Steffensen, 2015. "Optimal consumption, investment and life insurance with surrender option guarantee," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2015(1), pages 59-87, January.
    11. Gemmo, Irina & Rogalla, Ralph & Weinert, Jan-Hendrik, 2020. "Optimal portfolio choice with tontines under systematic longevity risk," Annals of Actuarial Science, Cambridge University Press, vol. 14(2), pages 302-315, September.
    12. 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).
    13. Richard, Scott F., 1975. "Optimal consumption, portfolio and life insurance rules for an uncertain lived individual in a continuous time model," Journal of Financial Economics, Elsevier, vol. 2(2), pages 187-203, June.
    14. Peng, Xingchun & Li, Baihui, 2023. "Optimal investment, consumption and life insurance purchase with learning about return predictability," Insurance: Mathematics and Economics, Elsevier, vol. 113(C), pages 70-95.
    15. Nicole Branger & An Chen & Antje Mahayni & Thai Nguyen, 2023. "Optimal collective investment: an analysis of individual welfare," Mathematics and Financial Economics, Springer, volume 17, number 5, December.
    16. Larry G. Epstein & Stanley E. Zin, 2013. "Substitution, risk aversion and the temporal behavior of consumption and asset returns: A theoretical framework," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 12, pages 207-239, World Scientific Publishing Co. Pte. Ltd..
    17. Dagpunar, John, 2021. "Closed-form solutions for an explicit modern ideal tontine with bequest motive," Insurance: Mathematics and Economics, Elsevier, vol. 100(C), pages 261-273.
    18. Chen, An & Hieber, Peter & Rach, Manuel, 2021. "Optimal retirement products under subjective mortality beliefs," Insurance: Mathematics and Economics, Elsevier, vol. 101(PA), pages 55-69.
    19. Xie, Lin & Chen, Lv & Qian, Linyi & Li, Danping & Yang, Zhixin, 2023. "Optimal investment and consumption strategies for pooled annuity with partial information," Insurance: Mathematics and Economics, Elsevier, vol. 108(C), pages 129-155.
    20. Ng, Tak Wa & Nguyen, Thai, 2025. "Pareto efficiency and financial fairness under limited expected loss constraint," Journal of Mathematical Economics, Elsevier, vol. 117(C).
    21. Weir, David R., 1989. "Tontines, Public Finance, and Revolution in France and England, 1688–1789," The Journal of Economic History, Cambridge University Press, vol. 49(1), pages 95-124, March.
    22. Kihlstrom, Richard, 2009. "Risk aversion and the elasticity of substitution in general dynamic portfolio theory: Consistent planning by forward looking, expected utility maximizing investors," Journal of Mathematical Economics, Elsevier, vol. 45(9-10), pages 634-663, September.
    23. Milevsky, Moshe A. & Salisbury, Thomas S., 2015. "Optimal retirement income tontines," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 91-105.
    24. 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.
    25. Ng, Tak Wa & Nguyen, Thai, 2023. "Portfolio performance under benchmarking relative loss and portfolio insurance: From omega ratio to loss aversion," ASTIN Bulletin, Cambridge University Press, vol. 53(1), pages 149-183, January.
    26. Jensen, N.R. & Steffensen, M., 2015. "Personal finance and life insurance under separation of risk aversion and elasticity of substitution," Insurance: Mathematics and Economics, Elsevier, vol. 62(C), pages 28-41.
    27. Chen, An & Rach, Manuel, 2019. "Options on tontines: An innovative way of combining tontines and annuities," Insurance: Mathematics and Economics, Elsevier, vol. 89(C), pages 182-192.
    28. Hieber, Peter & Lucas, Nathalie, 2022. "Modern Life-Care Tontines," ASTIN Bulletin, Cambridge University Press, vol. 52(2), pages 563-589, May.
    29. An Chen & Thai Nguyen, 2024. "Risk management under weighted limited expected loss," Quantitative Finance, Taylor & Francis Journals, vol. 24(5), pages 593-612, May.
    30. 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.
    31. Thomas Bernhardt & Catherine Donnelly, 2019. "Modern tontine with bequest: innovation in pooled annuity products," Papers 1903.05990, arXiv.org.
    32. Barajas-Paz, Andres & Donnelly, Catherine, 2023. "An attribution analysis of investment risk sharing in collective defined contribution schemes," Annals of Actuarial Science, Cambridge University Press, vol. 17(2), pages 385-414, July.
    33. Takeshi Yagihashi & Juan Du, 2015. "Intertemporal elasticity of substitution and risk aversion: are they related empirically?," Applied Economics, Taylor & Francis Journals, vol. 47(15), pages 1588-1605, March.
    34. 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.
    35. Denuit, Michel & Hieber, Peter & Robert, Christian Y., 2022. "Mortality Credits Within Large Survivor Funds," ASTIN Bulletin, Cambridge University Press, vol. 52(3), pages 813-834, September.
    36. Michel Denuit & Raluca Vernic, 2018. "Bivariate Bernoulli Weighted Sums and Distribution of Single-Period Tontine Benefits," Methodology and Computing in Applied Probability, Springer, vol. 20(4), pages 1403-1416, December.
    37. Chen, An & Nguyen, Thai & Stadje, Mitja, 2018. "Optimal investment under VaR-Regulation and Minimum Insurance," Insurance: Mathematics and Economics, Elsevier, vol. 79(C), pages 194-209.
    38. 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.
    39. Denuit, Michel & Hieber, Peter & Robert, Christian Y., 2022. "Mortality credits within large survivor funds," LIDAM Reprints ISBA 2022030, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    40. Denuit, Michel & Vernic, Raluca, 2018. "Bivariate Bernoulli Weighted Sums and Distribution of Single-Period Tontine Benefits," LIDAM Reprints ISBA 2018032, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    41. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
    42. Bernhardt, Thomas & Donnelly, Catherine, 2019. "Modern tontine with bequest: Innovation in pooled annuity products," Insurance: Mathematics and Economics, Elsevier, vol. 86(C), pages 168-188.
    43. Han, Nan-wei & Hung, Mao-wei, 2012. "Optimal asset allocation for DC pension plans under inflation," Insurance: Mathematics and Economics, Elsevier, vol. 51(1), pages 172-181.
    44. Bruno Bouchard & Huyên Pham, 2004. "Wealth-path dependent utility maximization in incomplete markets," Finance and Stochastics, Springer, vol. 8(4), pages 579-603, November.
    45. Donnelly, Catherine & Guillén, Montserrat & Nielsen, Jens Perch, 2013. "Exchanging uncertain mortality for a cost," Insurance: Mathematics and Economics, Elsevier, vol. 52(1), pages 65-76.
    46. repec:dau:papers:123456789/1803 is not listed on IDEAS
    47. Moshe A. Milevsky & Thomas S. Salisbury, 2025. "The Riccati tontine: how to satisfy regulators on average," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 50(1), pages 72-102, March.
    48. Cox, John C. & Huang, Chi-fu, 1989. "Optimal consumption and portfolio policies when asset prices follow a diffusion process," Journal of Economic Theory, Elsevier, vol. 49(1), pages 33-83, October.
    49. 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.
    50. 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.
    51. 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.
    52. 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.
    53. Donnelly, Catherine, 2015. "Actuarial Fairness And Solidarity In Pooled Annuity Funds," ASTIN Bulletin, Cambridge University Press, vol. 45(1), pages 49-74, January.
    54. Nielsen, Peter Holm & Steffensen, Mogens, 2008. "Optimal investment and life insurance strategies under minimum and maximum constraints," Insurance: Mathematics and Economics, Elsevier, vol. 43(1), pages 15-28, August.
    55. 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).
    56. An Chen & Linyi Qian & Zhixin Yang, 2021. "Tontines with mixed cohorts," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2021(5), pages 437-455, May.
    57. Chen, An & Chen, Yusha & Xu, Xian, 2022. "Care-dependent tontines," Insurance: Mathematics and Economics, Elsevier, vol. 106(C), pages 69-89.
    58. 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).
    59. John Dagpunar, 2020. "Closed-form Solutions for an Explicit Modern Ideal Tontine with Bequest Motive," Papers 2005.00715, arXiv.org, revised Jun 2021.
    60. Thomas Bernhardt & Ge Qu, 2024. "Wealth heterogeneity in a closed pooled annuity fund," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2024(3), pages 199-226, March.
    61. Boulier, Jean-Francois & Huang, ShaoJuan & Taillard, Gregory, 2001. "Optimal management under stochastic interest rates: the case of a protected defined contribution pension fund," Insurance: Mathematics and Economics, Elsevier, vol. 28(2), pages 173-189, April.
    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. Tim J. Boonen & Kenneth Tsz Hin Ng & Tak Wa Ng & Thai Nguyen, 2026. "Pareto and Bowley Reinsurance Games in Peer-to-Peer Insurance," Papers 2602.14223, 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. Moshe A. Milevsky & Thomas S. Salisbury, 2025. "The Riccati tontine: how to satisfy regulators on average," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 50(1), pages 72-102, March.
    2. 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.
    3. Carole Bernard & Marco Feliciangeli & Steven Vanduffel, 2025. "Can an actuarially unfair tontine be optimal?," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 50(1), pages 39-71, March.
    4. Denuit, Michel & Robert, Christian Y., 2023. "Endowment contingency funds for mutual aid and public financing," LIDAM Discussion Papers ISBA 2023009, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    5. An Chen & Alexander Muermann & Casey Rothschild, 2025. "Tontines and their modern (re)discovery," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 50(1), pages 1-5, March.
    6. Hieber, Peter & Lucas, Nathalie, 2020. "Life-Care Tontines," LIDAM Discussion Papers ISBA 2020026, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    7. An Chen & Thai Nguyen & Thorsten Sehner, 2022. "Unit-Linked Tontine: Utility-Based Design, Pricing and Performance," Risks, MDPI, vol. 10(4), pages 1-27, April.
    8. Chen, An & Guillen, Montserrat & Rach, Manuel, 2021. "Fees in tontines," Insurance: Mathematics and Economics, Elsevier, vol. 100(C), pages 89-106.
    9. Bégin, Jean-François & Sanders, Barbara, 2024. "Benefit volatility-targeting strategies in lifetime pension pools," Insurance: Mathematics and Economics, Elsevier, vol. 118(C), pages 72-94.
    10. Hanbali, Hamza, 2025. "Mean-variance longevity risk-sharing for annuity contracts," Insurance: Mathematics and Economics, Elsevier, vol. 120(C), pages 207-235.
    11. Moshe A. Milevsky & Thomas S. Salisbury & Robyn Allen, 2025. "Equitable Longevity Risk Sharing or, the raison d'\^etre for a First Nations Pension Plan," Papers 2512.00122, arXiv.org.
    12. Chen, An & Hieber, Peter & Rach, Manuel, 2021. "Optimal retirement products under subjective mortality beliefs," Insurance: Mathematics and Economics, Elsevier, vol. 101(PA), pages 55-69.
    13. Xie, Lin & Chen, Lv & Qian, Linyi & Li, Danping & Yang, Zhixin, 2023. "Optimal investment and consumption strategies for pooled annuity with partial information," Insurance: Mathematics and Economics, Elsevier, vol. 108(C), pages 129-155.
    14. Maria Aragona & Luca Regis & Elena Vigna, 2024. "A Redistributive GSA Scheme to Cope With Socio-Economic Mortality Differentials," Carlo Alberto Notebooks 732 JEL Classification: C, Collegio Carlo Alberto.
    15. Dhaene, Jan & Milevsky, Moshe A., 2024. "Egalitarian pooling and sharing of longevity risk a.k.a. can an administrator help skin the tontine cat?," Insurance: Mathematics and Economics, Elsevier, vol. 119(C), pages 238-250.
    16. Dagpunar, John, 2021. "Closed-form solutions for an explicit modern ideal tontine with bequest motive," Insurance: Mathematics and Economics, Elsevier, vol. 100(C), pages 261-273.
    17. Doreen Kabuche & Michael Sherris & Andrés M. Villegas & Jonathan Ziveyi, 2025. "Return smoothing in pooled annuity products," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 48(2), pages 933-970, December.
    18. Chen, An & Müller, Alfred & Rach, Manuel, 2025. "The tontine puzzle," Journal of Mathematical Economics, Elsevier, vol. 121(C).
    19. Thomas Bernhardt & Catherine Donnelly, 2020. "Quantifying the trade-off between income stability and the number of members in a pooled annuity fund," Papers 2010.16009, arXiv.org.
    20. Shuanglan Li & Héloïse Labit Hardy & Michael Sherris & Andrés M. Villegas, 2022. "A Managed Volatility Investment Strategy for Pooled Annuity Products," Risks, MDPI, vol. 10(6), pages 1-30, June.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D14 - Microeconomics - - Household Behavior - - - Household Saving; Personal Finance
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies
    • G23 - Financial Economics - - Financial Institutions and Services - - - Non-bank Financial Institutions; Financial Instruments; Institutional Investors

    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:125:y:2025:i:c:s0167668725001088. 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.