The master equation for large population equilibriums

Springer Proceedings in Mathematics and Statistics

Volumn 100, Issue , 2014, Pages 77-128

  Carmona, René ^a   Delarue, François ^b  

^a PRINCETON UNIVERSITY   (United States)

^b UNIVERSITÉ DE NICE SOPHIA ANTIPOLIS   (France)

Author keywords

[No Author keywords available]

Indexed keywords

DIFFERENTIAL EQUATIONS; OPTIMIZATION; STOCHASTIC CONTROL SYSTEMS; STOCHASTIC SYSTEMS;

CONDITIONAL DISTRIBUTION; DETERMINISTIC FUNCTIONS; FORWARD-BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS; HAMILTON-JACOBI-BELLMAN EQUATIONS; OPTIMIZATION PROBLEMS; PROBABILISTIC INTERPRETATION; STOCHASTIC DIFFERENTIAL EQUATIONS; STOCHASTIC PARTIAL DIFFERENTIAL EQUATION;

VLASOV EQUATION;

EID: 84919448149     PISSN: 21941009     EISSN: 21941017     Source Type: Conference Proceeding    
DOI: 10.1007/978-3-319-11292-3_4     Document Type: Conference Paper

References (20)

1. A. Bensoussan, J. Frehse, P. Yam, The master equation in mean-field theory. Technical report. http://arxiv.org/abs/1404.4150
2. P. Cardaliaguet, Notes on mean field games. Notes from P.L. Lions’ lectures at the Collège de France https://www.ceremade.dauphine.fr/cardalia/MFG100629.pdf (2012)
3. R. Carmona, F. Delarue, Forward-backward stochastic differential equations and controlled McKean Vlasov dynamics. in Annals of Probability To appear
4. R. Carmona, F. Delarue, Probabilistic analysis of mean field games. SIAM J. Control Optim. 51, 2705–2734 (2013)
5. R. Carmona, F. Delarue, D. Lacker, Mean field games with a common noise. Technical report. http://arxiv.org/abs/1407.6181
6. R. Carmona, F. Delarue, A. Lachapelle, Control of McKean-Vlasov versus mean field games. Math. Financ. Econ. 7, 131–166 (2013)
7. R. Carmona, J.P. Fouque, A. Sun, Mean field games and systemic risk. To appear in Communications in Mathematical Sciences
8. J.F. Chassagneux, D. Crisan, F. Delarue, McKean-Vlasov FBSDEs and relatedmaster equation. Work in progress
9. W. Fleming, M. Soner, Controlled Markov Processes and Viscosity Solutions (Springer, New York, 2010)
10. D.A. Gomes, J. Saude, Mean field games models—a brief survey. Technical report (2013)
11. O. Guéant, J.M. Lasry, P.L. Lions, Paris Princeton Lectures in Mathematical Finance IV, in Mean Field Games and Applications, Lecture Notes in Mathematics, ed. by R. Carmona, et al. (Springer, Berlin, 2010)
12. M. Huang, P.E. Caines, R.P. Malhamé, Large population stochastic dynamic games: closedloop McKean-Vlasov systems and the Nash certainty equivalence principle. Commun. Inf. Syst. 6, 221–252 (2006)
13. J.M. Lasry, P.L. Lions, Jeux à champ moyen I. Le cas stationnaire. Comptes Rendus de l’Académie des Sciences de Paris, ser. A 343(9), 619–625 (2006)
14. J.M. Lasry, P.L. Lions, Jeux à champ moyen II. Horizon fini et contrôle optimal. Comptes Rendus de l’Académie des Sciences de Paris, ser. A 343(10), 679–684 (2006)
15. J.M. Lasry, P.L. Lions, Mean field games. Jpn. J. Math. 2(1), 229–260 (2007)
16. P.L. Lions, Théorie des jeux à champs moyen et applications. Technical report, 2007–2008
17. J. Ma, H. Yin, J. Zhang, On non-Markovian forward-backward SDEs and backward stochastic PDEs. Stoch. Process. Appl. 122, 3980–4004 (2012)
18. D. Nualart, The Malliavin Calculus and Related Topics, Probability and its Applications (Springer, New York, 1995)
19. S. Peng, Stochastic Hamilton Jacobi Bellman equations. SIAM J. Control Optim. 30, 284–304 (1992)
20. A.S. Sznitman, Topics in propagation of chaos, in D.L. Burkholder et al., Ecole de Probabilités de Saint Flour, XIX-1989. Lecture Notes in Mathematics, vol. 1464 (Springer, Heidelberg, 1989), pp. 165–251