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Hier finden Sie wissenschaftliche Publikationen aus den FraunhoferInstituten. Firstorder sensitivity of the optimal value in a Markov decision model with respect to deviations in the transition probability function
 Mathematical methods of operations research 92 (2020), No.1, pp.165197 ISSN: 14322994 ISSN: 03409422 

 English 
 Journal Article, Electronic Publication 
 Fraunhofer IVI () 
Abstract
Markov decision models (MDM) used in practical applications are most often less complex than the underlying ‘true’ MDM. The reduction of model complexity is performed for several reasons. However, it is obviously of interest to know what kind of model reduction is reasonable (in regard to the optimal value) and what kind is not. In this article we propose a way how to address this question. We introduce a sort of derivative of the optimal value as a function of the transition probabilities, which can be used to measure the (firstorder) sensitivity of the optimal value w.r.t. changes in the transition probabilities. ‘Differentiability’ is obtained for a fairly broad class of MDMs, and the ‘derivative’ is specified explicitly. Our theoretical findings are illustrated by means of optimization problems in inventory control and mathematical finance.