TY - CHAP
T1 - An optimal threshold policy in applications of a two-state markov process
AU - Khmelnitsky, Eugene
N1 - Publisher Copyright:
© Springer International Publishing Switzerland 2014.
PY - 2014
Y1 - 2014
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84955073180&partnerID=8YFLogxK
U2 - 10.1007/978-3-319-00669-7_11
DO - 10.1007/978-3-319-00669-7_11
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AN - SCOPUS:84955073180
T3 - International Series in Operations Research and Management Science
SP - 203
EP - 219
BT - International Series in Operations Research and Management Science
PB - Springer New York LLC
ER -