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Numerical solution of a long-term average control problem for singular stochastic processes

Author

Listed:
  • P. Kaczmarek
  • S. Kent
  • G. Rus
  • R. Stockbridge
  • B. Wade

Abstract

This paper analyzes numerically a long-term average stochastic control problem involving a controlled diffusion on a bounded region. The solution technique takes advantage of an infinite-dimensional linear programming formulation for the problem which relates the stationary measures to the generators of the diffusion. The restriction of the diffusion to an interval is accomplished through reflection at one end point and a jump operator acting singularly in time at the other end point. Different approximations of the linear program are obtained using finite differences for the differential operators (a Markov chain approximation to the diffusion) and using a finite element method to approximate the stationary density. The numerical results are compared with each other and with dynamic programming. Copyright Springer-Verlag 2007

Suggested Citation

  • P. Kaczmarek & S. Kent & G. Rus & R. Stockbridge & B. Wade, 2007. "Numerical solution of a long-term average control problem for singular stochastic processes," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 66(3), pages 451-473, December.
    • Handle: RePEc:spr:mathme:v:66:y:2007:i:3:p:451-473
    DOI: 10.1007/s00186-007-0166-9
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    References listed on IDEAS

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    1. ,, 2001. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 17(6), pages 1157-1160, December.
    2. K. Helmes & R. H. Stockbridge, 2000. "Numerical Comparison of Controls and Verification of Optimality for Stochastic Control Problems," Journal of Optimization Theory and Applications, Springer, vol. 106(1), pages 107-127, July.
    3. ,, 2001. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 17(5), pages 1025-1031, October.
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    1. R. Stockbridge, 2014. "Discussion of dynamic programming and linear programming approaches to stochastic control and optimal stopping in continuous time," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 77(1), pages 137-162, January.

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