Optimal stochastic control methods are used to examine decumulation strategies for a defined contribution (DC) plan retiree. An initial investment horizon of 15 years is considered, since the retiree will attain this age with high probability. The objective function reward measure is the expected sum of the withdrawals. The objective function tail risk measure is the expected linear shortfall with respect to a desired lower bound for wealth at 15 years. The lower bound wealth level is the amount which is required to fund a lifelong annuity 15 years after retirement, which generates the required minimum cash flows. This ameliorates longevity risk. The controls are the withdrawal amount each year, and the asset allocation strategy. Maximum and minimum withdrawal amounts are specified. Specifying a short initial decumulation horizon, results in the optimal strategy achieving: (i) median withdrawals at the maximum rate within 2–3 years of retirement (ii) terminal wealth larger than the desired lower bound at 15 years, with greater than 90% probability and (iii) median terminal wealth at 15 years considerably larger than the desired lower bound. The controls are computed using a parametric model of historical stock and bond returns, and then tested in bootstrap resampled simulations using historical data. At the 15 year investment horizon, the retiree has the option of (i) continuing to self-manage the decumulation policy or (ii) purchasing an annuity.

中文翻译：

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DC 计划投资者的两阶段递减策略

最优随机控制方法用于检查固定缴款 (DC) 计划退休人员的累积策略。考虑到 15 年的初始投资期限，因为退休人员很有可能达到这个年龄。目标函数奖励度量是提款的预期总和。目标函数尾部风险度量是相对于 15 年财富期望下限的预期线性短缺。下限财富水平是为退休后 15 年的终身年金提供资金所需的金额，从而产生所需的最低现金流。这改善了长寿风险。控制是每年的提款金额和资产配置策略。规定了最大和最小提款金额。指定一个较短的初始累积范围，90%概率和 (iii) 15 年的终端财富中值远大于期望的下限。使用历史股票和债券回报的参数模型计算控制，然后使用历史数据在引导重采样模拟中进行测试。在 15 年的投资期限内，退休人员可以选择 (i) 继续自行管理减免政策或 (ii) 购买年金。