Existence of Strict Optimal Controls for Long-term Average Stochastic Control Problems

Abstract : Convexity conditions are identified under which optimal controls in the class of strict controls exist for a large class of stochastic processes under a long-term average criterion in the presence of hard and/or soft constraints. The result adapts a similar result obtained by Haussmann and Lepeltier (1990) for a controlled diffusion under a mixed optimal- stopping/finite-horizon/first-exit criterion. The approach taken in this paper is to utilize an equivalent linear programming formulation of the control problem. These results apply to controlled processes such as diffusions, Markov chains, sim- ple Markov jump processes, diffusions with jumps, regime- switching diffusions and solutions to L ́ evy stochastic differential equations.
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Communication dans un congrès
19th International Symposium on Mathematical Theory of Networks and Systems - MTNS 2010, Jul 2010, Budapest, Hungary. 2010
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Contributeur : François Dufour <>
Soumis le : mercredi 29 janvier 2014 - 10:52:57
Dernière modification le : jeudi 11 janvier 2018 - 06:22:11

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  • HAL Id : hal-00938169, version 1

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François Dufour, Richard H. Stockbridge. Existence of Strict Optimal Controls for Long-term Average Stochastic Control Problems. 19th International Symposium on Mathematical Theory of Networks and Systems - MTNS 2010, Jul 2010, Budapest, Hungary. 2010. 〈hal-00938169〉

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