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Closed-form solutions for an explicit modern ideal tontine with bequest motive

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  • Dagpunar, John

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.

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  • 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.
    • Handle: RePEc:eee:insuma:v:100:y:2021:i:c:p:261-273
    DOI: 10.1016/j.insmatheco.2021.05.008
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    References listed on IDEAS

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    9. Thomas Bernhardt & Catherine Donnelly, 2019. "Modern tontine with bequest: innovation in pooled annuity products," Papers 1903.05990, arXiv.org.
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    14. Donnelly, Catherine, 2015. "Actuarial Fairness And Solidarity In Pooled Annuity Funds," ASTIN Bulletin, Cambridge University Press, vol. 45(1), pages 49-74, January.
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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.

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    More about this item

    Keywords

    Defined contribution pension; Tontines; Constant relative risk aversion; Dynamic consumption economics; Bequest motive;
    All these keywords.

    JEL classification:

    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C41 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Duration Analysis; Optimal Timing Strategies
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • D14 - Microeconomics - - Household Behavior - - - Household Saving; Personal Finance
    • D15 - Microeconomics - - Household Behavior - - - Intertemporal Household Choice; Life Cycle Models and Saving

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