OPTIMAL STOPPING WITH EXPECTATION CONSTRAINTS

被引:2
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
相关论文
共 50 条
[31]   Solving optimal stopping problems under model uncertainty via empirical dual optimisation [J].
Belomestny, Denis ;
Huebner, Tobias ;
Kraetschmer, Volker .
FINANCE AND STOCHASTICS, 2022, 26 (03) :461-503
[32]   ROBUST RETIREMENT WITH RETURN AMBIGUITY: OPTIMAL G-STOPPING TIME IN DUAL SPACE [J].
Park, Kyunghyun ;
Wong, Hoi Ying .
SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2023, 61 (03) :1009-1037
[33]   A Nonparametric Algorithm for Optimal Stopping Based on Robust Optimization [J].
Sturt, Bradley .
OPERATIONS RESEARCH, 2023, 71 (05) :1530-1557
[34]   An exactly solvable multiple stochastic optimal stopping problem [J].
Hidekazu Yoshioka .
Advances in Difference Equations, 2018
[35]   Application of Optimal Stopping Theory to Pandemic Lockdown Policies [J].
El Hassan, Noura ;
Maddah, Bacel ;
Ben Abdelaziz, Fouad .
2022 INTERNATIONAL CONFERENCE ON DECISION AID SCIENCES AND APPLICATIONS (DASA), 2022, :779-783
[36]   An exactly solvable multiple stochastic optimal stopping problem [J].
Yoshioka, Hidekazu .
ADVANCES IN DIFFERENCE EQUATIONS, 2018,
[37]   CONSTRUCTION OF THE VALUE FUNCTION AND OPTIMAL RULES IN OPTIMAL STOPPING OF ONE-DIMENSIONAL DIFFUSIONS [J].
Helmes, Kurt ;
Stockbridge, Richard H. .
ADVANCES IN APPLIED PROBABILITY, 2010, 42 (01) :158-182
[38]   DYNAMIC PROGRAMMING EQUATION FOR THE MEAN FIELD OPTIMAL STOPPING PROBLEM [J].
Talbi, Mehdi ;
Touzi, Nizar ;
Zhang, Jianfeng .
SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2023, 61 (04) :2140-2164
[39]   OPTIMAL STOPPING PROBLEM FOR STOCHASTIC DIFFERENTIAL EQUATIONS WITH RANDOM COEFFICIENTS [J].
Chang, Mou-Hsiung ;
Pang, Tao ;
Yong, Jiongmin .
SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2009, 48 (02) :941-971
[40]   On the strict value of the non-linear optimal stopping problem [J].
Grigorova, Miryana ;
Imkeller, Peter ;
Ouknine, Youssef ;
Quenez, Marie-Claire .
ELECTRONIC COMMUNICATIONS IN PROBABILITY, 2020, 25 :1-9