关于模型不确定性随机控制问题强形式的一个注记
A note on the strong formulation of stochastic control problems with model uncertainty
摘要：
考虑一类具有模型不确定性的马尔可夫随机控制问题。控制器（智能玩家）只观察状态，因此使用反馈（闭环）策略。对收益没有直接兴趣的不利参与者（自然）选择开环控制，使不确定性参数化。这在反馈策略和开环控制上创建了两步最优化问题（就像游戏的一半）。主要结果是表明，在某些假设下，这提供了相同的价值（一半）的零和对称对策，其中不利的球员也发挥反馈策略，并积极地试图最大限度地减少回报。价值函数独立于不利参与者可访问的过滤。除了建模问题之外，本说明是[S] 3b的技术伴侣。
英文摘要：
We consider a Markovian stochastic control problem with model uncertainty. The controller (intelligent player) observes only the state, and, therefore, uses feed-back (closed-loop) strategies. The adverse player (nature) who does not have a direct interest in the pay-off, chooses open-loop controls that parametrize Knightian uncertainty. This creates a two-step optimization problem (like half of a game) over feed-back strategies and open-loop controls. The main result is to show that, under some assumptions, this provides the same value as the (half of) the zero-sum symmetric game where the adverse player also plays feed-back strategies and actively tries to minimize the pay-off. The value function is independent of the filtration accessible to the adverse player. Aside from the modeling issue, the present note is a technical companion to [SÎ3b].
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
