Geodesic
Controlled diffusion mean field games with common noise and McKean--Vlasov second order backward SDE
Teoriâ veroâtnostej i ee primeneniâ, Tome 66 (2021) no. 4, pp. 774-805

Voir la notice de l'article provenant de la source Math-Net.Ru

We consider a mean field game with common noise in which the diffusion coefficients may be controlled. We prove existence of a weak relaxed solution under some continuity conditions on the coefficients. We then show that, when there is no common noise, the solution of this mean field game is characterized by a McKean–Vlasov type second order backward SDE.
Keywords: stochastic control, Nash equilibrium, mean field game, exterior noise. 
@article{TVP_2021_66_4_a8,
     author = {A. Barrasso and N. Touzi},
     title = {Controlled diffusion mean field games with common noise and {McKean--Vlasov} second order backward {SDE}},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {774--805},
     publisher = {mathdoc},
     volume = {66},
     number = {4},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2021_66_4_a8/}
}
TY  - JOUR
AU  - A. Barrasso
AU  - N. Touzi
TI  - Controlled diffusion mean field games with common noise and McKean--Vlasov second order backward SDE
JO  - Teoriâ veroâtnostej i ee primeneniâ
PY  - 2021
SP  - 774
EP  - 805
VL  - 66
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TVP_2021_66_4_a8/
LA  - ru
ID  - TVP_2021_66_4_a8
ER  - 
%0 Journal Article
%A A. Barrasso
%A N. Touzi
%T Controlled diffusion mean field games with common noise and McKean--Vlasov second order backward SDE
%J Teoriâ veroâtnostej i ee primeneniâ
%D 2021
%P 774-805
%V 66
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TVP_2021_66_4_a8/
%G ru
%F TVP_2021_66_4_a8
A. Barrasso; N. Touzi. Controlled diffusion mean field games with common noise and McKean--Vlasov second order backward SDE. Teoriâ veroâtnostej i ee primeneniâ, Tome 66 (2021) no. 4, pp. 774-805. http://geodesic.mathdoc.fr/item/TVP_2021_66_4_a8/