An Optimal Threshold Policy in Applications of a Two-State Markov Process

Eugene Khmelnitsky ()
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Eugene Khmelnitsky: Tel-Aviv University

A chapter in Models and Methods in Economics and Management Science, 2014, pp 203-219 from Springer

Abstract: Abstract We consider a problem of optimal control of a two-state Markov process. The objective is to minimize a total discounted cost over an infinite horizon, when the capabilities of the control effort are different in the two states. The necessary optimality conditions allow studying state-costate dynamics over the regular and singular control regimes. By making use of the properties of the costate process we prove the optimality of a threshold policy and calculate the value of the threshold in some specific cases of the cost function, as well as in a case where a probabilistic constraint is imposed on the state variable. The distribution function of the state variable and the thresholds are expressed as a series of the modified Bessel functions.

Keywords: Modify Bessel Function; Threshold Policy; Basic Consumption; Costate Dynamic; Control Markov Chain (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:isochp:978-3-319-00669-7_11

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DOI: 10.1007/978-3-319-00669-7_11

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