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

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.

Date: 2020-05, Revised 2021-06
New Economics Papers: this item is included in nep-age, nep-gen and nep-upt
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Published in Insurance: Mathematics and Economics Volume 100, September 2021, Pages 261-273

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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:2005.00715

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