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

John Dagpunar

Insurance: Mathematics and Economics, 2021, vol. 100, issue C, 261-273

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.

Keywords: Defined contribution pension; Tontines; Constant relative risk aversion; Dynamic consumption economics; Bequest motive (search for similar items in EconPapers)
JEL-codes: C41 C58 C61 D14 D15 G22 (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:100:y:2021:i:c:p:261-273

DOI: 10.1016/j.insmatheco.2021.05.008

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