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.

我们将固定缴款 (DC) 养老金计划的递减策略作为最优随机控制中的一个问题。控制是提款金额和资产分配策略。我们对提款金额施加最大和最小限制，对资产配置策略施加无卖空无杠杆限制。我们的目标函数将奖励衡量为在减持期内的预期总提款，风险通过减免期结束时的预期短缺（ES）来衡量。我们基于市场随机过程的参数模型以数值方式解决随机控制问题。我们发现，与固定的恒定提款策略相比，将最小提款设置为恒定提款金额，最优策略具有显着更高的预期平均提款，以 ES 风险的微小增加为代价。对自举重采样历史市场数据的测试表明，该策略对参数模型错误规范具有鲁棒性。