论文标题
一种动态分析方法，用于风险有感染的受控Martingale问题
A dynamic analytic method for risk-aware controlled martingale problems
论文作者
论文摘要
我们提出了一种新的，可拖动的方法，用于解决和分析有限和无限，折扣时代的风险感受控制问题，其中受控过程的动态被描述为Martingale问题。我们假设波兰的状态和动作空间，并使用通用，放松的控制措施，我们陈述了一种风险感知的动态最佳控制问题，即最大程度地减少通用风险功能描述的成本风险。然后，我们构建了一种替代公式，该公式采用了非线性编程问题的形式，它受动态，{i.e。}时间依赖性和线性kolmogorov方程的约束，描述了状态和累积成本的分布。我们表明该配方是等效的，并且可以将最佳控制过程视为在受控过程状态，运行成本和时间中。我们进一步证明，在其他条件下，达到了最佳价值。提出和解决了一个示例数字问题。
We present a new, tractable method for solving and analyzing risk-aware control problems over finite and infinite, discounted time-horizons where the dynamics of the controlled process are described as a martingale problem. Supposing general Polish state and action spaces, and using generalized, relaxed controls, we state a risk-aware dynamic optimal control problem of minimizing risk of costs described by a generic risk function. We then construct an alternative formulation that takes the form of a nonlinear programming problem, constrained by the dynamic, {i.e.} time-dependent, and linear Kolmogorov forward equation describing the distribution of the state and accumulated costs. We show that the formulations are equivalent, and that the optimal control process can be taken to be Markov in the controlled process state, running costs, and time. We further prove that under additional conditions, the optimal value is attained. An example numeric problem is presented and solved.
