Capacities, Measurable Selection and Dynamic Programming Part II: Application in Stochastic Control Problems
Optimization and Control
2024-10-03 v3
Abstract
We provide an overview on how to use the measurable selection techniques to derive the dynamic programming principle for a general stochastic optimal control/stopping problem. By considering its martingale problem formulation on the canonical space of paths, one can check the required measurability conditions. This covers in particular the most classical controlled/stopped diffusion processes problems. Further, we study the approximation property of the optimal control problems by piecewise constant control problems. As a byproduct, we obtain an equivalence result of the strong, weak and relaxed formulations of the controlled/stopped diffusion processes problem.
Cite
@article{arxiv.1310.3364,
title = {Capacities, Measurable Selection and Dynamic Programming Part II: Application in Stochastic Control Problems},
author = {Nicole El Karoui and Xiaolu Tan},
journal= {arXiv preprint arXiv:1310.3364},
year = {2024}
}