固定缴款计划递减的随机控制方法：“金融中最棘手、最困难的问题”
A Stochastic Control Approach to Defined Contribution Plan Decumulation: "The Nastiest, Hardest Problem in Finance"
摘要：
本文将固定缴款养老金计划的累积策略问题归结为最优随机控制问题。控制是提取金额和资产配置策略。我们对提取金额施加了最大和最小限制，并对资产配置策略施加了无做空无杠杆限制。我们的目标函数的回报措施的预期总提款在递减期，和风险衡量的预期损失（ES）在递减期结束。我们解决了随机控制问题的数值，基于市场随机过程的参数模型。我们发现，相比于一个固定的常数提取策略，最小提取设置为常数提取量，最优策略有一个显着更高的预期平均提取，在ES风险的成本非常小的增加。对自举重采样历史市场数据的测试表明，该策略对参数模型的错误设定具有鲁棒性。
英文摘要：
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.
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