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A Numerical Method for Solving Singular Stochastic Control Problems

Graduate School of Business, Stanford University, Stanford, California 94305
School of Industrial Engineering, Purdue University, West Lafayette, Indiana 47907
skumar{at}stanford.edu
kumar{at}purdue.edu

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.

Subject classifications: dynamic programming/optimal control; singular stochastic control; HJB equations; numerical methods; probability; diffusions; queueing; scheduling; Brownian approximations; economics; investments under uncertainty.
History: Received January 2002; revision received April 2003; accepted May 2003.

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