Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika
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Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika, 2020, Number 4, Pages 3–11 (Mi vmumm4335)  
This article is cited in 1 scientific paper (total in 1 paper)

Mathematics

On certain analytically solvable problems of mean field games theory

S. I. Nikulin, O. S. Rozanova

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
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Abstract: 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.
Key words: mean field games theory, Riccati equations, exact solutions, portfolio selection.
Funding agency Grant number
Moscow Center of Fundamental and Applied Mathematics
Received: 27.02.2020
English version:
Moscow University Mathematics Bulletin, 2020, Volume 75, Issue 4, Pages 139–148
DOI: https://doi.org/10.3103/S002713222004004X
Bibliographic databases:
Document Type: Article
UDC: 511
Language: Russian
Citation: S. I. Nikulin, O. S. Rozanova, “On certain analytically solvable problems of mean field games theory”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2020, no. 4, 3–11; Moscow University Mathematics Bulletin, 75:4 (2020), 139–148
Citation in format AMSBIB
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\jour Moscow University Mathematics Bulletin
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\pages 139--148
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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