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A Mean-Field Model of Optimal Investment

Author

Listed:
  • Calvia, Alessandro

    (Center for Mathematical Economics, Bielefeld University)

  • Federico, Salvatore

    (Center for Mathematical Economics, Bielefeld University)

  • Ferrari, Giorgio

    (Center for Mathematical Economics, Bielefeld University)

  • Gozzi, Fausto

    (Center for Mathematical Economics, Bielefeld University)

Abstract

We establish the existence and uniqueness of the equilibrium for a stochastic mean-field game of optimal investment. The analysis covers both finite and infinite time horizons, and the mean-field interaction of the representative company with a mass of identical and indistinguishable firms is modeled through the time-dependent price at which the produced good is sold. At equilibrium, this price is given in terms of a nonlinear function of the expected (optimally controlled) production capacity of the representative company at each time. The proof of the existence and uniqueness of the mean-field equilibrium relies on a priori estimates and the study of nonlinear integral equations, but employs different techniques for the finite and infinite horizon cases. Additionally, we investigate the deterministic counterpart of the mean-field game under study.

Suggested Citation

  • Calvia, Alessandro & Federico, Salvatore & Ferrari, Giorgio & Gozzi, Fausto, 2024. "A Mean-Field Model of Optimal Investment," Center for Mathematical Economics Working Papers 690, Center for Mathematical Economics, Bielefeld University.
    • Handle: RePEc:bie:wpaper:690
    as

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    File URL: https://pub.uni-bielefeld.de/download/2988384/2988387
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    References listed on IDEAS

    as
    1. A. Bensoussan & K. C. J. Sung & S. C. P. Yam & S. P. Yung, 2016. "Linear-Quadratic Mean Field Games," Journal of Optimization Theory and Applications, Springer, vol. 169(2), pages 496-529, May.
    2. Erzo G. J. Luttmer, 2007. "Selection, Growth, and the Size Distribution of Firms," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 122(3), pages 1103-1144.
    3. Rinel Foguen Tchuendom, 2018. "Uniqueness for Linear-Quadratic Mean Field Games with Common Noise," Dynamic Games and Applications, Springer, vol. 8(1), pages 199-210, March.
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    Keywords

    mean-field games; mean-field equilibrium; forward-backward ODEs; optimal investment; price formation;
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