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A General Stochastic Maximum Principle for SDEs of Mean-field Type
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.ORCID iD: 0000-0002-6608-0715
2011 (English)In: Applied mathematics and optimization, ISSN 0095-4616, E-ISSN 1432-0606, Vol. 64, no 2, 197-216 p.Article in journal (Refereed) Published
Abstract [en]

We study the optimal control for stochastic differential equations (SDEs) of mean-field type, in which the coefficients depend on the state of the solution process as well as of its expected value. Moreover, the cost functional is also of mean-field type. This makes the control problem time inconsistent in the sense that the Bellman optimality principle does not hold. For a general action space a Peng's-type stochastic maximum principle (Peng, S.: SIAM J. Control Optim. 2(4), 966-979, 1990) is derived, specifying the necessary conditions for optimality. This maximum principle differs from the classical one in the sense that here the first order adjoint equation turns out to be a linear mean-field backward SDE, while the second order adjoint equation remains the same as in Peng's stochastic maximum principle.

Place, publisher, year, edition, pages
2011. Vol. 64, no 2, 197-216 p.
Keyword [en]
Stochastic control, Maximum principle, Mean-field SDE, McKean-Vlasov equation, Time inconsistent control
National Category
Probability Theory and Statistics
URN: urn:nbn:se:kth:diva-37535DOI: 10.1007/s00245-011-9136-yISI: 000293235100003ScopusID: 2-s2.0-80052971337OAI: diva2:434901
QC 20110816Available from: 2011-08-16 Created: 2011-08-15 Last updated: 2011-08-16Bibliographically approved

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Djehiche, Boualem
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