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Optimal Control versus Stochastic Target problems: An Equivalence Result

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Date
2012
Dewey
Probabilités et mathématiques appliquées
Sujet
Stochastic target; stochastic control; viscosity solutions
Journal issue
Systems & Control Letters
Volume
61
Number
2
Publication date
2012
Article pages
343-346
Publisher
Elsevier
DOI
http://dx.doi.org/10.1016/j.sysconle.2011.11.010
URI
https://basepub.dauphine.fr/handle/123456789/5482
Collections
  • CEREMADE : Publications
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Author
Bouchard, Bruno
Dang, Ngoc Minh
Type
Article accepté pour publication ou publié
Abstract (EN)
Within a general abstract framework, we show that any optimal control problem instandard form can be translated into a stochastic target problem as de ned in [17], whenever the underlying ltered probability space admits a suitable martingale representationproperty. This provides a uni ed way of treating these two classes of stochastic con-trol problems. As an illustration, we show, within a jump di usion framework, how theHamilton-Jacobi-Bellman equations associated to an optimal control problem in standard form can be easily retrieved from the partial di erential equations associated to itsstochastic target counterpart.

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