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Optimality necessary conditions in singular stochastic control problems with nonsmooth data
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.ORCID iD: 0000-0002-6608-0715
2009 (English)In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 355, no 2, 479-494 p.Article in journal (Refereed) Published
Abstract [en]

The present paper studies the stochastic maximum principle in singular optimal control, where the state is governed by a stochastic differential equation With nonsmooth coefficients, allowing both classical control and singular control. The proof of the main result is based oil the approximation of the initial problem, by a sequence of control problems with smooth coefficients. We, then apply Ekeland's variational principle for this approximating sequence of control problems, in order to establish necessary conditions satisfied by a sequence of near optimal controls. Finally, we prove the convergence of the scheme, using Krylov's inequality in the nondegenerate case and the Bouleau-Hirsch now property in the degenerate one. The adjoint process obtained is given by means of distributional derivatives of the coefficients.

Place, publisher, year, edition, pages
2009. Vol. 355, no 2, 479-494 p.
Keyword [en]
Stochastic differential equation, Stochastic control, Maximum, principle, Singular control, Distributional derivative, Adjoint, process, Variational principle, maximum principle, coefficients
Identifiers
URN: urn:nbn:se:kth:diva-18417DOI: 10.1016/j.jmaa.2009.01.066ISI: 000265982800003Scopus ID: 2-s2.0-62549139160OAI: oai:DiVA.org:kth-18417DiVA: diva2:336464
Note
QC 20100525Available from: 2010-08-05 Created: 2010-08-05 Last updated: 2010-12-13Bibliographically approved

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Djehiche, Boualem

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