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Average optimal switching of a Markov chain with a Borel state space

Author

Listed:
  • Alexander Yushkevich
  • Evgueni Gordienko

Abstract

We extend results on average per unit time optimality criterion in a switching model from a countable state space to a Borel state space. In the model we consider, a controller selects an increasing sequence of stopping times with respect to a Markov chain, and gets rewards and pays costs at them in an alternating order. The rewards and costs depend on the state of the chain. We find the optimal average gain and construct an optimal strategy. The basic tool is a variational problem with two obstacles that appears also in Dynkin games. Copyright Springer-Verlag Berlin Heidelberg 2002

Suggested Citation

  • Alexander Yushkevich & Evgueni Gordienko, 2002. "Average optimal switching of a Markov chain with a Borel state space," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 55(1), pages 143-159, March.
    • Handle: RePEc:spr:mathme:v:55:y:2002:i:1:p:143-159
    DOI: 10.1007/s001860200178
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    Cited by:

    1. Randall Martyr, 2014. "Solving finite time horizon Dynkin games by optimal switching," Papers 1411.4438, arXiv.org, revised Jan 2016.
    2. Pavel V. Gapeev, 2016. "Bayesian Switching Multiple Disorder Problems," Mathematics of Operations Research, INFORMS, vol. 41(3), pages 1108-1124, August.

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