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 providing income under specified bequest motive, from defined contribution pension pot. A key feature present is that it relaxes assumption fixed proportions invested in tontine accounts. making proportion an additional control function obtain, hitherto unavailable, closed-form solutions for fractional consumption rate, wealth, amount, constant relative risk averse utility. show optimal product optimum rate exponentiated parameter. certain circumstances, such very high life-cycle utility maximisation strategy will necessitate negative mortality credits analogous to member paying life insurance premiums. Typical scenarios are explored using UK Office National Statistics tables.