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2014

The Master Equation in Mean Field Theory

Bensoussan, Alain, Frehse, Jens, Yam, Phillip

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In his lectures at College de France, P.L.

Lions introduced the concept of Master equation, see [5] for Mean Field Games.
It is introduced in a heuristic fashion, from the system of partial differential equations, associated to a Nash equilibrium for a large, but finite, number of players.
The method, also explained in[2], consists in a formal analogy of terms.

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Peng S.G., Stochastic Hamilton-Jacobi-Bellman Equations, (1992), SIAM J. Control and Optimization
Original
1992
Earlier work this paper cites.
Lasry J.M., Lions P.L. , (2007) Mean Field Games, Japanese Journal of Mathematics
2007
Earlier work this paper cites.
Bensoussan A., Sung K.C.J., Yam S.C.P., and Yung S. P., (2011) Linear Quadratic Mean Field Games, Arxiv
2011
Earlier work this paper cites.

Similar

Bensoussan A. , Frehse J. , Yam S.C.P., (2013) Mean Field Games and Mean Field Type Control Theory, Springer Briefs in Mathematics, N.Y. , Heidelberg, Dordrecht, London
2013
Cited alongside, same era.
Cardaliaguet P. , (2013) Notes on P.L. Lions’ lectures at the College de France, Working Paper, September
2013
Cited alongside, same era.
Carmona R., Delarue F., (2014) The Master Equation for Large Population Equilibriums, Arxiv
2014
Cited alongside, same era.
Lions P.L. , Lectures at College de France, http://www.college-de-france.fr
Cited in the paper.

Then

Carmona R., Fouque J.P., Sun L.H., (2014) Mean Field Games and Systemic Risk, to appear in Communications in Mathematical Sciences
2014
Closest in time.
Laurière M., Pironneau O., (2014) Dynamic Programming for Mean Field Type Control, submitted to C. R. Acad. Sci. Paris Sr. I Math
2014
Closest in time.

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