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Singular Control and Optimal Stopping of SPDEs, and Backward SPDEs with Reflection

Abstract : We consider general singular control problems for random fields given by a stochastic partial differential equation (SPDE). We show that under some conditions the optimal singular control can be identified with the solution of a coupled system of SPDE and a reflected backward SPDE (RBSPDE). As an illustration we apply the result to a singular optimal harvesting problem from a population whose density is modeled as a stochastic reaction-diffusion equation. Existence and uniqueness of solutions of RBSPDEs are established, as well as comparison theorems. We then establish a relation between RBSPDEs and optimal stopping of SPDEs, and apply the result to a risk-minimizing stopping problem.
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https://hal.inria.fr/hal-00919136
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Submitted on : Monday, December 16, 2013 - 1:35:26 PM
Last modification on : Wednesday, February 26, 2020 - 7:06:15 PM
Long-term archiving on: : Tuesday, March 18, 2014 - 4:25:27 PM

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Bernt Øksendal, Agnès Sulem, Tusheng Zhang. Singular Control and Optimal Stopping of SPDEs, and Backward SPDEs with Reflection. Mathematics of Operations Research, INFORMS, 2013. ⟨hal-00919136⟩

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