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

Closed-form solutions for an explicit modern ideal tontine with bequest motive
Closed-form solutions for an explicit modern ideal tontine with bequest motive
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.
0167-6687
261-273
Dagpunar, John
be796c6f-4b91-462b-b7ef-c9387efc26dc
Dagpunar, John
be796c6f-4b91-462b-b7ef-c9387efc26dc

Dagpunar, John (2021) Closed-form solutions for an explicit modern ideal tontine with bequest motive. Insurance: Mathematics and Economics, 100 (10), 261-273. (doi:10.1016/j.insmatheco.2021.05.008).

Record type: Article

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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Accepted/In Press date: 29 May 2021
Published date: 17 June 2021

Identifiers

Local EPrints ID: 468984
URI: http://eprints.soton.ac.uk/id/eprint/468984
ISSN: 0167-6687
PURE UUID: c65d102f-49d0-4f7a-b34d-8d70933a5139

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Date deposited: 02 Sep 2022 19:03
Last modified: 02 Sep 2022 19:03

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