Open Access
October 2020 Pathwise stochastic control with applications to robust filtering
Andrew L. Allan, Samuel N. Cohen
Ann. Appl. Probab. 30(5): 2274-2310 (October 2020). DOI: 10.1214/19-AAP1558


We study the problem of pathwise stochastic optimal control, where the optimization is performed for each fixed realisation of the driving noise, by phrasing the problem in terms of the optimal control of rough differential equations. We investigate the degeneracy phenomenon induced by directly controlling the coefficient of the noise term, and propose a simple procedure to resolve this degeneracy whilst retaining dynamic programming. As an application, we use pathwise stochastic control in the context of stochastic filtering to construct filters which are robust to parameter uncertainty, demonstrating an original application of rough path theory to statistics.


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Andrew L. Allan. Samuel N. Cohen. "Pathwise stochastic control with applications to robust filtering." Ann. Appl. Probab. 30 (5) 2274 - 2310, October 2020.


Received: 1 February 2019; Revised: 1 June 2019; Published: October 2020
First available in Project Euclid: 15 September 2020

MathSciNet: MR4149529
Digital Object Identifier: 10.1214/19-AAP1558

Primary: 60H99 , 93E11 , 93E20

Keywords: parameter uncertainty , rough HJB equation , Rough paths , Stochastic control , stochastic filtering

Rights: Copyright © 2020 Institute of Mathematical Statistics

Vol.30 • No. 5 • October 2020
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