Singular Control and Optimal Stopping of SPDEs, and Backward SPDEs with Reflection - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Mathematics of Operations Research Year : 2013

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

Agnès Sulem
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Tusheng Zhang
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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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Dates and versions

hal-00919136 , version 1 (16-12-2013)

Identifiers

  • HAL Id : hal-00919136 , version 1

Cite

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