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Closed-form Solutions for an Explicit Modern Ideal Tontine with Bequest Motive

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  • John Dagpunar

Abstract

In this paper I extend the work of Bernhardt and Donnelly (2019) dealing with modern explicit tontines, as a way of providing income under a specified bequest motive, from a defined contribution pension pot. A key feature of the present paper is that it relaxes the assumption of fixed proportions invested in tontine and bequest accounts. In making the bequest proportion an additional control function I obtain, hitherto unavailable, closed-form solutions for the fractional consumption rate, wealth, bequest amount, and bequest proportion under a constant relative risk averse utility. I show that the optimal bequest proportion is the product of the optimum fractional consumption rate and an exponentiated bequest parameter. I show that under certain circumstances, such as a very high bequest motive, a life-cycle utility maximisation strategy will necessitate negative mortality credits analogous to a member paying life insurance premiums. Typical scenarios are explored using UK Office of National Statistics life tables.

Suggested Citation

  • John Dagpunar, 2020. "Closed-form Solutions for an Explicit Modern Ideal Tontine with Bequest Motive," Papers 2005.00715, arXiv.org, revised Jun 2021.
  • Handle: RePEc:arx:papers:2005.00715
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-257, August.
    4. 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.
    5. Thomas Bernhardt & Catherine Donnelly, 2019. "Modern tontine with bequest: innovation in pooled annuity products," Papers 1903.05990, arXiv.org.
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    Cited by:

    1. Lin He & Zongxia Liang & Sheng Wang, 2022. "Modern Tontine with Transaction Costs," Papers 2209.09709, arXiv.org, revised Jun 2023.
    2. Moshe A. Milevsky & Thomas S. Salisbury, 2024. "The Riccati Tontine: How to Satisfy Regulators on Average," Papers 2402.14555, arXiv.org.

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