Abstract
Only a small number of DPs possess an explicit solution. Therefore structural (i.e. qualitative) properties of the value functions and maximizers are of considerable importance. Here we study the monotonicity of V n (s) in n and, with arbitrary relations on S, also in s. Examples of structural properties considered in later sections are concavity and Lipschitz continuity of the value function. As a first benefit of each structural result it can serve to check the correctness of numerical computations. Further benefits, specific to the structure considered, are discussed at the corresponding place.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Beckmann, M. J. (1968). Dynamic programming of economic decisions. New York: Springer.
Hinderer, K. (1985). On the structure of solutions of stochastic dynamic programs. In Proceedings of the seventh conference on probability theory (Braşov, 1982) (pp. 173–182). Utrecht: VNU Science Press.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing AG
About this chapter
Cite this chapter
Hinderer, K., Rieder, U., Stieglitz, M. (2016). Monotonicity of the Value Functions. In: Dynamic Optimization. Universitext. Springer, Cham. https://doi.org/10.1007/978-3-319-48814-1_6
Download citation
DOI: https://doi.org/10.1007/978-3-319-48814-1_6
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-48813-4
Online ISBN: 978-3-319-48814-1
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)