Bequest-Motivated Decumulation of UK Pensions for Non-Domiciled Individuals: A Monte-Carlo and HJB Approach
By Sebastien Hitier
We study the optimal decumulation of a UK pension pot for an expatriate holder who is tax-resident in a jurisdiction that does not tax investment income or gifts. Because the pension wrapper offers no ongoing tax shelter to heirs, the holder’s sole objective is to minimise the expected present value of lifetime taxes-personal income tax on drawdowns plus inheritance tax at death. We formulate the problem as a stochastic optimal control with Gompertz-Makeham mortality, progressive UK taxation, and geometric Brownian motion for the real pot value. A Monte-Carlo framework first compares parametric withdrawal policies and demonstrates that aggressive early drawdowns can reduce expected combined tax by nearly 90% relative to a conventional 4% rule. We then derive the Hamilton-Jacobi-Bellman equation and solve it numerically by explicit finite differences in log-wealth coordinates. The resulting optimal policy w ⋆ (t, P) varies systematically with pot size and age: it prescribes full withdrawal for small pots (to exploit the personal allowance) and for very large pots (to avoid punitive inheritance tax), with a gradual drawdown at intermediate sizes that increases as the pension holder ages. The HJB solution confirms the parametric results and delivers a precise, optimal adapted withdrawal schedule.
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