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

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. Typical scenarios are explored using UK Office of National Statistics life tables, showing the behaviour of these characteristics under varying degrees of constant relative risk aversion.

More information

Identifiers

Catalogue record

Export record