A numerical method for solving singular stochastic control problems

A numerical method for solving singular stochastic control problems

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Article ID: iaor20073836
Country: United States
Volume: 52
Issue: 4
Start Page Number: 563
End Page Number: 582
Publication Date: Jul 2004
Journal: Operations Research
Authors: ,
Keywords: programming: dynamic, scheduling, queues: applications
Abstract:

Singular stochastic control has found diverse applications in operations management, economics, and finance. However, in all but the simplest of cases, singular stochastic control problems cannot be solved analytically. In this paper, we propose a method for numerically solving a class of singular stochastic control problems. We combine finite element methods that numerically solve partial differential equations with a policy update procedure based on the principle of smooth pasting to iteratively solve Hamilton–Jacobi–Bellman equations associated with the stochastic control problem. A key feature of our method is that the presence of singular controls simplifies the procedure. We illustrate the method on two examples of singular stochastic control problems, one drawn from economics and the other from queueing systems.

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