Stochastic control/stopping problem with expectation constraints

Erhan Bayraktar and Song Yao

Stochastic Processes and their Applications, 2024, vol. 176, issue C

Abstract: We study a stochastic control/stopping problem with a series of inequality-type and equality-type expectation constraints in a general non-Markovian framework. We demonstrate that the stochastic control/stopping problem with expectation constraints (CSEC) is independent of a specific probability setting and is equivalent to the constrained stochastic control/stopping problem in weak formulation (an optimization over joint laws of Brownian motion, state dynamics, diffusion controls and stopping rules on an enlarged canonical space). Using a martingale-problem formulation of controlled SDEs in spirit of Stroock and Varadhan (2006), we characterize the probability classes in weak formulation by countably many actions of canonical processes, and thus obtain the upper semi-analyticity of the CSEC value function. Then we employ a measurable selection argument to establish a dynamic programming principle (DPP) in weak formulation for the CSEC value function, in which the conditional expected costs act as additional states for constraint levels at the intermediate horizon.

Keywords: Stochastic control/stopping problem with expectation constraints; Martingale-problem formulation; Enlarged canonical space; Polish space of diffusion controls; Polish space of stopping times; Dynamic programming principle; Regular conditional probability distribution; Measurable selection (search for similar items in EconPapers)
Date: 2024
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spa.2024.104430

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