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Controlled one dimensional diffusions with switching costs--average cost criterion

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  • Doshi, Bharat T.

Abstract

This paper deals with a one-dimensional controlled diffusion process on a compact interval with reflecting boundaries. The set of available actions is finite and the action can be changed only at countably many stopping times. The cost structure includes both a continuous movement cost rate depending on the state and the action, and a switching cost when the action is changed. The policies are evaluated with respect to the average cost criterion. The problem is solved by looking at, for each stationary policy, an embedded stochastic process corresponding to the state intervals visited in the sequence of switching times. The communicating classes of this process are classified into closed and transient groups and a method of calculating the average cost for the closed and transient classes is given. Also given are conditions to guarantee the optimality of a stationary policy. A Brownian motion control problem with quadratic cost is worked out in detail and the form of an optimal policy is established.

Suggested Citation

  • Doshi, Bharat T., 1978. "Controlled one dimensional diffusions with switching costs--average cost criterion," Stochastic Processes and their Applications, Elsevier, vol. 8(2), pages 211-227, December.
    • Handle: RePEc:eee:spapps:v:8:y:1978:i:2:p:211-227
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    Cited by:

    1. Klosterhalfen, Steffen T. & Holzhauer, Falk & Fleischmann, Moritz, 2018. "Control of a continuous production inventory system with production quantity restrictions," European Journal of Operational Research, Elsevier, vol. 268(2), pages 569-581.

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