Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/288279 
Year of Publication: 
2020
Citation: 
[Journal:] Mathematical Methods of Operations Research [ISSN:] 1432-5217 [Volume:] 92 [Issue:] 1 [Publisher:] Springer [Place:] Berlin, Heidelberg [Year:] 2020 [Pages:] 165-197
Publisher: 
Springer, Berlin, Heidelberg
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 (first-order) 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.
Subjects: 
Markov decision model
Model reduction
Transition probability function
Optimal value
Functional differentiability
Financial optimization
Persistent Identifier of the first edition: 
Creative Commons License: 
cc-by Logo
Document Type: 
Article
Document Version: 
Published Version

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