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Blackwell Optimality for Controlled Diffusion Processes

Part of: Stochastic systems and control Markov processes

Published online by Cambridge University Press:  14 July 2016

Héctor Jasso-Fuentes  and
Onésimo Hernández-Lerma
Héctor Jasso-Fuentes*
Affiliation:
CINVESTAV
Onésimo Hernández-Lerma*
Affiliation:
CINVESTAV
*
∗Postal address: Department of Mathematics, CINVESTAV-IPN, A. Postal 14-740, Mexico DF 07000, Mexico.
∗Postal address: Department of Mathematics, CINVESTAV-IPN, A. Postal 14-740, Mexico DF 07000, Mexico.
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Abstract

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In this paper we study m-discount optimality (m ≥ −1) and Blackwell optimality for a general class of controlled (Markov) diffusion processes. To this end, a key step is to express the expected discounted reward function as a Laurent series, and then search certain control policies that lexicographically maximize the mth coefficient of this series for m = −1,0,1,…. This approach naturally leads to m-discount optimality and it gives Blackwell optimality in the limit as m → ∞.

Keywords

Controlled diffusionsaverage rewardLaurent seriessensitive discount optimalityBlackwell optimality

MSC classification

Secondary: 93E20: Optimal stochastic control 60J60: Diffusion processes
Type
Research Article
Information
Journal of Applied Probability , Volume 46 , Issue 2 , June 2009 , pp. 372 - 391
Copyright
Copyright © Applied Probability Trust 2009 

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