Controlled reflected SDEs and Neumann problem for backward SPDEs
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Publication:2286452
DOI10.1214/19-AAP1465zbMATH Open1439.60053arXiv1706.06284OpenAlexW2980706492MaRDI QIDQ2286452
Author name not available (Why is that?)
Publication date: 22 January 2020
Published in: (Search for Journal in Brave)
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 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.
Full work available at URL: https://arxiv.org/abs/1706.06284
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