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October 2019 Controlled reflected SDEs and Neumann problem for backward SPDEs
Erhan Bayraktar, Jinniao Qiu
Ann. Appl. Probab. 29(5): 2819-2848 (October 2019). DOI: 10.1214/19-AAP1465

Abstract

We solve the optimal control problem of a one-dimensional reflected stochastic differential equation, whose coefficients can be path dependent. The value function of this problem is characterized by a backward stochastic partial differential equation (BSPDE) with Neumann boundary conditions. We prove the existence and uniqueness of a sufficiently regular solution for this BSPDE, which is then used to construct the optimal feedback control. In fact, we prove a more general result: the existence and uniqueness of strong solution for the Neumann problem for general nonlinear BSPDEs, which might be of interest even out of the current context.

Citation

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Erhan Bayraktar. Jinniao Qiu. "Controlled reflected SDEs and Neumann problem for backward SPDEs." Ann. Appl. Probab. 29 (5) 2819 - 2848, October 2019. https://doi.org/10.1214/19-AAP1465

Information

Received: 1 August 2018; Published: October 2019
First available in Project Euclid: 18 October 2019

zbMATH: 07155060
MathSciNet: MR4019876
Digital Object Identifier: 10.1214/19-AAP1465

Subjects:
Primary: 60H15, 60K35, 91G80, 93E20

Rights: Copyright © 2019 Institute of Mathematical Statistics

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Vol.29 • No. 5 • October 2019
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