A Framework for the Dynamic Programming Principle and Martingale-generated Control Correspondences
Optimization and Control
2019-06-04 v2 Probability
Abstract
We construct an abstract framework in which the dynamic programming principle (DPP) can be readily proven. It encompasses a broad range of common stochastic control problems in the weak formulation, and deals with problems in the "martingale formulation" with particular ease. We give two illustrations; first, we establish the DPP for general controlled diffusions and show that their value functions are viscosity solutions of the associated Hamilton-Jacobi-Bellman equations under minimal conditions. After that, we show how to treat singular control on the example of the classical monotone-follower problem.
Cite
@article{arxiv.1801.10218,
title = {A Framework for the Dynamic Programming Principle and Martingale-generated Control Correspondences},
author = {Roman Fayvisovich and Gordan Zitkovic},
journal= {arXiv preprint arXiv:1801.10218},
year = {2019}
}