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Equilibrium Pricing of Securities in the Co-Presence of Cooperative and Non-Cooperative Populations

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  • Masaaki Fujii

    (Faculty of Economics, The University of Tokyo)

Abstract

In this work, we develop an equilibrium model for price formation of securities in a market composed of two populations of different types: the first one consists of cooperative agents, while the other one consists of non-cooperative agents. The trading of every cooperative member is assumed to be coordinated by a central planner. In the large population limit, the problem for the central planner is shown to be a conditional extended mean-field control. In addition to the convexity assumptions, if the relative size of the cooperative population is small enough, then we are able to show the existence of a unique equilibrium for both the finite-agent and the mean-field models. The strong convergence to the mean-field model is also proved under the same conditions.

Suggested Citation

  • Masaaki Fujii, 2022. "Equilibrium Pricing of Securities in the Co-Presence of Cooperative and Non-Cooperative Populations," CIRJE F-Series CIRJE-F-1201, CIRJE, Faculty of Economics, University of Tokyo.
    • Handle: RePEc:tky:fseres:2022cf1201
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    File URL: http://www.cirje.e.u-tokyo.ac.jp/research/dp/2022/2022cf1201.pdf
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    References listed on IDEAS

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    Cited by:

    1. Masaaki Fujii & Masashi Sekine, 2023. "Mean-field Equilibrium Price Formation with Exponential Utility," CIRJE F-Series CIRJE-F-1210, CIRJE, Faculty of Economics, University of Tokyo.
    2. Masaaki Fujii & Masashi Sekine, 2023. "Mean-field equilibrium price formation with exponential utility," Papers 2304.07108, arXiv.org, revised Oct 2023.
    3. Masaaki Fujii & Masashi Sekine, 2023. "Mean-field equilibrium price formation with exponential utility," CARF F-Series CARF-F-559, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    4. David Evangelista & Yuri Thamsten, 2023. "Approximately optimal trade execution strategies under fast mean-reversion," Papers 2307.07024, arXiv.org, revised Aug 2023.

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