Maximum Principle for Stochastic Control of SDEs with Measurable Drifts
Maximum Principle for Stochastic Control of SDEs with Measurable Drifts
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DOI：
10.1007/s10957-023-02209-0
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发表时间：
2021-01
影响因子：
1.9
通讯作者：
Olivier Menoukeu-Pamen;Ludovic Tangpi
中科院分区：
文献类型：
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作者：
Olivier Menoukeu-Pamen;Ludovic Tangpi
本文研究了具有非规则漂移系数的随机微分方程驱动系统的随机最优控制问题。我们建立了一个充分必要的随机最大值原理。为了实现这一点，我们首先推导出一个显式表示的第一个变化过程（在Sobolev意义上）的控制扩散。由于漂移系数是不光滑的，因此用状态过程的局部时表示。然后，我们构造了一个序列的最优控制问题的光滑系数的逼近论点。最后，我们使用Ekeland的变分原理，以获得一个近似的伴随过程，从中我们推导出的最大值原理，通过到极限。这项工作的主要动机是投资者支付财富税的最优消费问题。
In this paper, we consider stochastic optimal control of systems driven by stochastic differential equations with irregular drift coefficient. We establish a necessary and sufficient stochastic maximum principle. To achieve this, we first derive an explicit representation of the first variation process (in the Sobolev sense) of the controlled diffusion. Since the drift coefficient is not smooth, the representation is given in terms of the local time of the state process. Then we construct a sequence of optimal control problems with smooth coefficients by an approximation argument. Finally, we use Ekeland’s variational principle to obtain an approximating adjoint process from which we derive the maximum principle by passing to the limit. The work is notably motivated by the optimal consumption problem of investors paying wealth tax.