论文标题
与期望约束的最佳停止
Optimal Stopping with Expectation Constraints
论文作者
论文摘要
我们通过一系列不平等类型和等价期望限制在一般的非马克维亚框架中分析了一个最佳的停止问题。我们表明，在任意概率设置中与期望约束（OSEC）的最佳停止问题相当于弱公式中的受约束问题（对使用布朗运动和状态动力学在扩大规范空间上停止规则的联合定律优化），因此是OSEC值。使用Martingale-Promlem公式，我们在弱公式中对概率类进行等效表征，这意味着OSEC值函数的上半分析。然后，我们利用可测量的选择参数来建立OSEC值函数弱公式中的动态编程原理，其中有条件的预期成本在中间视野中充当约束水平的附加状态。
We analyze an optimal stopping problem with a series of inequality-type and equality-type expectation constraints in a general non-Markovian framework. We show that the optimal stopping problem with expectation constraints (OSEC) in an arbitrary probability setting is equivalent to the constrained problem in weak formulation (optimization over joint laws of stopping rules with Brownian motion and state dynamics on an enlarged canonical space) and thus the OSEC value. Using a martingale-problem formulation, we make an equivalent characterization of the probability classes in weak formulation, which implies that the OSEC value function s upper semi-analytic. Then we exploit a measurable selection argument to establish a dynamic programming principle in weak formulation for the OSEC value function, in which the conditional expected costs act as additional states for constraint levels at the intermediate horizon.
