We determine the optimal asset allocation to bonds and stocks using an annually recalculated virtual annuity (ARVA) spending rule for DC pension plan decumulation. Our objective function minimizes downside withdrawal variability for a given fixed value of total expected withdrawals. The optimal asset allocation is found using optimal stochastic control methods. We formulate the strategy as a solution to a Hamilton–Jacobi–Bellman (HJB) Partial Integro Differential Equation (PIDE). We impose realistic constraints on the controls (no-shorting, no-leverage, discrete rebalancing) and solve the HJB PIDEs numerically. Compared to a fixed-weight strategy which has the same expected total withdrawals, the optimal strategy has a much smaller average allocation to stocks and tends to de-risk rapidly over time. This conclusion holds in the case of a parametric model based on historical data and also in a bootstrapped market based on the historical data.

中文翻译：

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具有可变支出规则的 DC 养老金分摊的最佳资产分配

我们使用每年重新计算的虚拟年金 (ARVA) 支出规则来确定债券和股票的最佳资产配置，以进行 DC 养老金计划的累加。对于给定的总预期提款固定值，我们的目标函数将下行提款可变性最小化。使用最优随机控制方法找到最优资产配置。我们将该策略制定为 Hamilton-Jacobi-Bellman (HJB) 偏积分微分方程 (PIDE) 的解决方案。我们对控制施加现实约束（无短路、无杠杆、离散再平衡）并以数值方式求解 HJB PIDE。与具有相同预期总提款的固定权重策略相比，最优策略对股票的平均分配要小得多，并且随着时间的推移往往会迅速降低风险。