Stochastic control with rough paths
Probability
2013-05-21 v2 Optimization and Control
Abstract
We study a class of controlled rough differential equations. It is shown that the value function satisfies a HJB type equation; we also establish a form of the Pontryagin maximum principle. Deterministic problems of this type arise in the duality theory for controlled diffusion processes and typically involve anticipating stochastic analysis. We propose a formulation based on rough paths and then obtain a generalization of Roger's duality formula [L. C. G. Rogers, 2007] from discrete to continuous time. We also make the link to old work of [Davis--Burstein, 1987].
Cite
@article{arxiv.1303.7160,
title = {Stochastic control with rough paths},
author = {Joscha Diehl and Peter Friz and Paul Gassiat},
journal= {arXiv preprint arXiv:1303.7160},
year = {2013}
}