Geodesic
On certain analytically solvable problems of mean field games theory
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2020), pp. 3-11 
S. I. Nikulin; O. S. Rozanova. On certain analytically solvable problems of mean field games theory. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2020), pp. 3-11. http://geodesic.mathdoc.fr/item/VMUMM_2020_4_a0/
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     title = {On certain analytically solvable problems of mean field games theory},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2020_4_a0/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

We study the mean field games equations consisting of the coupled Kolmogorov–Fokker–Planck and Hamilton–Jacobi–Bellman equations. The equations are supplemented with initial and terminal conditions. It is shown that for a certain specific choice of data this problem can be reduced to solving a quadratically nonlinear ODE system. This situation occurs naturally in economic applications. As an example, the problem of forming an investor's opinion on an asset is considered.

[1] Guéant O., Lasry J.-M., Lions P.-L., “Mean Field Games and applications”, Paris–Princeton lectures on mathematical finance, Springer, Paris, 2010, 205–266 | MR

[2] Lasry J. M., Lions P.-L., “Mean field games”, Jap. J. Math., 2:1 (2007), 229–260 | DOI | MR | Zbl

[3] Gomes D. A., Saede J., “Mean field games models — A brief survey”, Dynamic Games and Appl., 4:2 (2013), 110–154 | DOI | MR

[4] Oksendal B., Stokhasticheskie differentsialnye uravneniya. Vvedenie v teoriyu i prilozheniya, Mir, M., 2003

[5] Cardaliaguet P., Notes on mean field games from P.-L. Lions' lectures at College de France, Paris, 2012 | MR

[6] Guéant O., “A reference case for mean field games models”, J. Math. Pures et. Appl., 92:3 (2009), 276–294 | DOI | MR | Zbl

[7] Merton R. C., Continuous time finance, Wiley-Blackwell, Oxford, U.K., 1992

[8] Ingersoll Jr., Jonathan E., Theory of financial decision making, Rowman and Littlefield, Totowa, NJ, 1987 | MR

[9] Bielecki T., Pliska S., Sherris M., “Risk sensitive asset allocation”, J. Econ. Dynamics and Control, 24 (2000), 1145–1177 | DOI | MR | Zbl