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

• 成果类型: Article
• 署名作者: Oksendal, Bernt; Sulem, Agnes; Zhang, Tusheng
• 署名单位: University of Oslo; Universite Gustave-Eiffel; University of Manchester
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2013.0602
• 发表日期: 2014
• 页码: 464-486
• 关键词: stochastic maximum principle; DIFFUSIONS

摘要

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.