A Numerical Method for Solving Singular Stochastic Control Problems
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 s...
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| Veröffentlicht in: | Operations research 2004-07, Vol.52 (4), p.563-582 |
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| creator | Kumar, Sunil Muthuraman, Kumar |
| description | 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. |
| doi_str_mv | 10.1287/opre.1030.0107 |
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| ispartof | Operations research, 2004-07, Vol.52 (4), p.563-582 |
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| subjects | Analysis Approximation Boundary conditions Brownian approximations Brownian motion Carrying costs Control theory Cost control diffusions Dynamic programming dynamic programming/optimal control economics HJB equations investments under uncertainty Mathematical procedures Mathematical vectors Methods Network servers Numerical methods Operations management Optimization Partial differential equations probability queueing Queuing scheduling singular stochastic control Stochastic models Stochastic processes Studies Technology application Terminator regions |
| title | A Numerical Method for Solving Singular Stochastic Control Problems |
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