caa a22 4500 445842164 CHVBK 20180317145348.0 cr unu---uuuuu 170323e20111001xx s 000 0 eng 10.1007/s00245-011-9136-y doi (NATIONALLICENCE)springer-10.1007/s00245-011-9136-y A General Stochastic Maximum Principle for SDEs of Mean-field Type [Elektronische Daten] [Rainer Buckdahn, Boualem Djehiche, Juan Li] 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. Springer Science+Business Media, LLC, 2011 Stochastic control nationallicence Maximum principle nationallicence Mean-field SDE nationallicence McKean-Vlasov equation nationallicence Time inconsistent control nationallicence Buckdahn Rainer Département de Mathématiques, Université de Bretagne Occidentale, 6, avenue Victor-le-Gorgeu, B.P. 809, 29285, Brest cedex, France aut Djehiche Boualem Department of Mathematics, Royal Institute of Technology, 100 44, Stockholm, Sweden aut Li Juan School of Mathematics and Statistics, Shandong University at Weihai, 264209, Weihai, P.R. China aut Applied Mathematics & Optimization Springer-Verlag 64/2(2011-10-01), 197-216 0095-4616 64:2<197 2011 64 245 https://doi.org/10.1007/s00245-011-9136-y text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00245-011-9136-y text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Buckdahn Rainer Département de Mathématiques, Université de Bretagne Occidentale, 6, avenue Victor-le-Gorgeu, B.P. 809, 29285, Brest cedex, France aut NATIONALLICENCE 700 1- Djehiche Boualem Department of Mathematics, Royal Institute of Technology, 100 44, Stockholm, Sweden aut NATIONALLICENCE 700 1- Li Juan School of Mathematics and Statistics, Shandong University at Weihai, 264209, Weihai, P.R. China aut NATIONALLICENCE 773 0- Applied Mathematics & Optimization Springer-Verlag 64/2(2011-10-01), 197-216 0095-4616 64:2<197 2011 64 245 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer