论文标题
一阶Pontryagin的最大原理用于规避风险的随机最佳控制问题
First-Order Pontryagin Maximum Principle for Risk-Averse Stochastic Optimal Control Problems
论文作者
论文摘要
在本文中，我们得出了符合最终不平等限制的最佳最佳控制问题的一阶最佳条件，其成本是一般的，可能是非平滑有限的有限相干风险措施。与涵盖这种情况的先前贡献不同，我们的分析适用于由标准布朗尼动作驱动的经典随机微分方程。此外，它提出了既不涉及二阶伴随方程式的优点，也没有导致所谓的弱版本的PMP，其中最大化相对于控制变量的最大化条件被汉密尔顿的平稳性代替。
In this paper, we derive first-order Pontryagin optimality conditions for risk-averse stochastic optimal control problems subject to final time inequality constraints, and whose costs are general, possibly non-smooth finite coherent risk measures. Unlike preexisting contributions covering this situation, our analysis holds for classical stochastic differential equations driven by standard Brownian motions. In addition, it presents the advantages of neither involving second-order adjoint equations, nor leading to the so-called weak version of the PMP, in which the maximization condition with respect to the control variable is replaced by the stationarity of the Hamiltonian.
