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August 2015 Randomized and backward SDE representation for optimal control of non-Markovian SDEs
Marco Fuhrman, Huyên Pham
Ann. Appl. Probab. 25(4): 2134-2167 (August 2015). DOI: 10.1214/14-AAP1045

Abstract

We study optimal stochastic control problems for non-Markovian stochastic differential equations (SDEs) where the drift, diffusion coefficients and gain functionals are path-dependent, and importantly we do not make any ellipticity assumptions on the SDE. We develop a control randomization approach and prove that the value function can be reformulated under a family of dominated measures on an enlarged filtered probability space. This value function is then characterized by a backward SDE with nonpositive jumps under a single probability measure, which can be viewed as a path-dependent version of the Hamilton–Jacobi–Bellman equation, and an extension to $G$-expectation.

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Marco Fuhrman. Huyên Pham. "Randomized and backward SDE representation for optimal control of non-Markovian SDEs." Ann. Appl. Probab. 25 (4) 2134 - 2167, August 2015. https://doi.org/10.1214/14-AAP1045

Information

Received: 1 November 2013; Revised: 1 April 2014; Published: August 2015
First available in Project Euclid: 21 May 2015

zbMATH: 1322.60087
MathSciNet: MR3349004
Digital Object Identifier: 10.1214/14-AAP1045

Subjects:
Primary: 60H10
Secondary: 93E20

Keywords: Backward stochastic differential equations , dominated measures , Non-Markovian controlled SDEs , randomization of controls

Rights: Copyright © 2015 Institute of Mathematical Statistics

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Vol.25 • No. 4 • August 2015
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