naa a22 4500 510808549 CHVBK 20180411083430.0 cr unu---uuuuu 180411e20130301xx s 000 0 eng 10.1007/s11579-012-0089-y doi (NATIONALLICENCE)springer-10.1007/s11579-012-0089-y Control of McKean-Vlasov dynamics versus mean field games [Elektronische Daten] [René Carmona, François Delarue, Aimé Lachapelle] We discuss and compare two investigation methods for the asymptotic regime of stochastic differential games with a finite number of players as the number of players tends to the infinity. These two methods differ in the order in which optimization and passage to the limit are performed. When optimizing first, the asymptotic problem is usually referred to as a mean-field game. Otherwise, it reads as an optimization problem over controlled dynamics of McKean-Vlasov type. Both problems lead to the analysis of forward-backward stochastic differential equations, the coefficients of which depend on the marginal distributions of the solutions. We explain the difference between the nature and solutions to the two approaches by investigating the corresponding forward-backward systems. General results are stated and specific examples are treated, especially when cost functionals are of linear-quadratic type. Springer-Verlag, 2012 Mean-field game nationallicence Controlled McKean-Vlasov stochastic differential equations nationallicence Forward-backward stochastic differential equations nationallicence Linear-quadratic nationallicence Cap-and-trade model nationallicence Carmona René ORFE, Bendheim Center for Finance, Princeton University, 08544, Princeton, NJ, USA aut Delarue François Laboratoire J.A. Dieudonné, Université de Nice Sophia-Antipolis, Parc Valrose, 06108, Nice Cedex 02, France aut Lachapelle Aimé ORFE, Bendheim Center for Finance, Princeton University, 08544, Princeton, NJ, USA aut Mathematics and Financial Economics Springer Berlin Heidelberg 7/2(2013-03-01), 131-166 1862-9679 7:2<131 2013 7 11579 https://doi.org/10.1007/s11579-012-0089-y text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11579-012-0089-y text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Carmona René ORFE, Bendheim Center for Finance, Princeton University, 08544, Princeton, NJ, USA aut NATIONALLICENCE 700 1- Delarue François Laboratoire J.A. Dieudonné, Université de Nice Sophia-Antipolis, Parc Valrose, 06108, Nice Cedex 02, France aut NATIONALLICENCE 700 1- Lachapelle Aimé ORFE, Bendheim Center for Finance, Princeton University, 08544, Princeton, NJ, USA aut NATIONALLICENCE 773 0- Mathematics and Financial Economics Springer Berlin Heidelberg 7/2(2013-03-01), 131-166 1862-9679 7:2<131 2013 7 11579 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer