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Some analytically solvable problems of the mean-field games theory

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  • Sergey I. Nikulin
  • Olga S. Rozanova

Abstract

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

Suggested Citation

  • Sergey I. Nikulin & Olga S. Rozanova, 2019. "Some analytically solvable problems of the mean-field games theory," Papers 1911.09441, arXiv.org.
    • Handle: RePEc:arx:papers:1911.09441
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    References listed on IDEAS

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    1. Bielecki, Tomasz R. & Pliska, Stanley R. & Sherris, Michael, 2000. "Risk sensitive asset allocation," Journal of Economic Dynamics and Control, Elsevier, vol. 24(8), pages 1145-1177, July.
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