  We pose the decumulation strategy for a Defined Contribution (DC) pension
plan as a problem in optimal stochastic control. The controls are the
withdrawal amounts and the asset allocation strategy. We impose maximum and
minimum constraints on the withdrawal amounts, and impose no-shorting
no-leverage constraints on the asset allocation strategy. Our objective
function measures reward as the expected total withdrawals over the
decumulation horizon, and risk is measured by Expected Shortfall (ES) at the
end of the decumulation period. We solve the stochastic control problem
numerically, based on a parametric model of market stochastic processes. We
find that, compared to a fixed constant withdrawal strategy, with minimum
withdrawal set to the constant withdrawal amount, the optimal strategy has a
significantly higher expected average withdrawal, at the cost of a very small
increase in ES risk. Tests on bootstrapped resampled historical market data
indicate that this strategy is robust to parametric model misspecification.
