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A note on bequest preferences in utility maximisation for modern tontines

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  • Thomas Bernhardt

Abstract

In this short note, we address two issues in the literature about modern tontines with bequest and utility maximisation: how to verify optimal controls and the decreasing allocation of funds in the tontine. We want to raise awareness in the actuarial community about the dual approach to solve optimal control problems when working with power utilities. Additionally, we point out that bequest preferences should be time-dependent or otherwise yield unrealistic investment strategies. We base our attempt at modelling bequest preferences on common sense rules like 100% payback upon death at the start that vanishes over time. Our modelling shows that the resulting investment strategy almost linearly adjusts the allocation in the tontine from 0% to 100% over time.

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  • Thomas Bernhardt, 2025. "A note on bequest preferences in utility maximisation for modern tontines," Papers 2501.08972, arXiv.org.
    • Handle: RePEc:arx:papers:2501.08972
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    References listed on IDEAS

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    1. Chen An & Rach Manuel, 2022. "Bequest-Embedded Annuities and Tontines," Asia-Pacific Journal of Risk and Insurance, De Gruyter, vol. 16(1), pages 1-46, January.
    2. Martin Herdegen & David Hobson & Joseph Jerome, 2021. "An elementary approach to the Merton problem," Mathematical Finance, Wiley Blackwell, vol. 31(4), pages 1218-1239, October.
    3. 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.
    4. Martin Herdegen & David Hobson & Joseph Jerome, 2020. "An elementary approach to the Merton problem," Papers 2006.05260, arXiv.org, revised Mar 2021.
    5. Stanley R. Pliska, 1986. "A Stochastic Calculus Model of Continuous Trading: Optimal Portfolios," Mathematics of Operations Research, INFORMS, vol. 11(2), pages 371-382, May.
    6. 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.
    7. Moshe A. Milevsky & Thomas S. Salisbury, 2024. "The Riccati Tontine: How to Satisfy Regulators on Average," Papers 2402.14555, arXiv.org.
    8. John Dagpunar, 2020. "Closed-form Solutions for an Explicit Modern Ideal Tontine with Bequest Motive," Papers 2005.00715, arXiv.org, revised Jun 2021.
    9. Thomas Bernhardt & Catherine Donnelly, 2019. "Modern tontine with bequest: innovation in pooled annuity products," Papers 1903.05990, arXiv.org.
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