OPTIMAL STOPPING WITH EXPECTATION CONSTRAINTS

被引:4
作者
Bayraktar, Erhan [1 ]
Yao, Song [2 ]
机构
[1] Univ Michigan, Dept Math, Ann Arbor, MI 48109 USA
[2] Univ Pittsburgh, Dept Math, Pittsburgh, PA 15260 USA
基金
美国国家科学基金会;
关键词
Optimal stopping with expectation constraints; martingale-problem formulation; enlarged canonical space; Polish space of stopping times; dynamic programming principle; regular conditional probability distribution; measurable selection; STOCHASTIC TARGET PROBLEMS; NONLINEAR EXPECTATIONS; DUALITY; GAMES; PART;
D O I
10.1214/23-AAP1980
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
020208 ; 070103 ; 0714 ;
摘要
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 (an optimization over joint laws of stopping rules with Brownian motion and state dynamics on an enlarged canonical space), and thus the OSEC value is independent of a specific probabilistic setup. Using a martingale-problem formulation, we make an equivalent characterization of the probability classes in weak formulation, which implies that the OSEC value function is upper semianalytic. 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.
引用
收藏
页码:917 / 959
页数:43
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