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arXiv · 1303.7160

Stochastic control with rough paths

Joscha Diehl·Peter Friz·Paul Gassiat
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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].

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Joscha Diehl, Peter Friz, Paul Gassiat. 2013-03-28. Stochastic control with rough paths. https://arxiv.org/abs/1303.7160

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