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Continuous-Time Mean Field Games with Finite StateSpace and Common Noise

Author

Listed:
  • Christoph Belak
  • Daniel Hoffmann
  • Frank T. Seifried

Abstract

We formulate and analyze a mathematical framework for continuous-time mean field gameswith finitely many states and common noise, including a rigorous probabilistic constructionof the state process. The key insight is that we can circumvent the master equation andreduce the mean field equilibrium to a system of forward-backward systems of (random)ordinary differential equations by conditioning on common noise events. In the absenceof common noise, our setup reduces to that of Gomes, Mohr and Souza [GMS13] andCecchin and Fischer [CF20].

Suggested Citation

  • Christoph Belak & Daniel Hoffmann & Frank T. Seifried, 2020. "Continuous-Time Mean Field Games with Finite StateSpace and Common Noise," Working Paper Series 2020-05, University of Trier, Research Group Quantitative Finance and Risk Analysis.
    • Handle: RePEc:trr:qfrawp:202005
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    File URL: https://www.uni-trier.de/fileadmin/fb4/prof/BWL/FIN/QFRA_Working_Papers/QFRA_20_05.pdf
    File Function: First version, 2020
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    References listed on IDEAS

    as
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    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    mean field games; common noise; Markov chains; regime shifts;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics

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