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Optimal switching problem for countable Markov chains: average reward criterion

Author

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  • Alexander Yushkevich

Abstract

Optimal switching we consider is the following generalization of optimal stopping: (i) there are a reward function and a cost function on the state space of a Markov chain; (ii) a controller selects stopping times sequentially; (iii) at those times the controller receives rewards and pays costs in an alternating order. In this paper we treat the case of a positive recurrent countable Markov chain and the average per unit time criterion. We find an optimal strategy and the maximal average gain in terms of the solution of a variational problem with two obstacles, known also in connection with Dynkin games. Copyright Springer-Verlag Berlin Heidelberg 2001

Suggested Citation

  • Alexander Yushkevich, 2001. "Optimal switching problem for countable Markov chains: average reward criterion," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 53(1), pages 1-24, April.
    • Handle: RePEc:spr:mathme:v:53:y:2001:i:1:p:1-24
    DOI: 10.1007/s001860000102
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    Cited by:

    1. Dabadghao, Shaunak S. & Chockalingam, Arun & Soltani, Taimaz & Fransoo, Jan, 2021. "Valuing Switching options with the moving-boundary method," Journal of Economic Dynamics and Control, Elsevier, vol. 127(C).
    2. Pavel Gapeev, 2006. "Multiple Disorder Problems for Wiener and Compound Poisson Processes With Exponential Jumps," SFB 649 Discussion Papers SFB649DP2006-074, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    3. Dabadghao, Shaunak S. & Chockalingam, Arun & Soltani, Taimaz & Fransoo, Jan C., 2021. "Valuing switching options with the moving-boundary method," Other publications TiSEM 45fe7e78-129f-4d41-ac2f-5, Tilburg University, School of Economics and Management.
    4. Per-Olov JOHANSSON & Bengt KRISTRÖM & Kaj NYSTRÖM, 2009. "On the evaluation of infrastructure investments: the case of electricity generation," Departmental Working Papers 2009-24, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.
    5. René Carmona & Savas Dayanik, 2008. "Optimal Multiple Stopping of Linear Diffusions," Mathematics of Operations Research, INFORMS, vol. 33(2), pages 446-460, May.
    6. 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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