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Broker-Trader Partial Information Nash Equilibria

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  • Xuchen Wu
  • Sebastian Jaimungal

Abstract

We study partial information Nash equilibrium between a broker and an informed trader. In this model, the informed trader, who possesses knowledge of a trading signal, trades multiple assets with the broker in a dealer market. Simultaneously, the broker trades these assets in a lit exchange where their actions impact the asset prices. The broker, however, only observes aggregate prices and cannot distinguish between underlying trends and volatility. Both the broker and the informed trader aim to maximize their penalized expected wealth. Using convex analysis, we characterize the Nash equilibrium and demonstrate its existence and uniqueness. Furthermore, we establish that this equilibrium corresponds to the solution of a nonstandard system of forward-backward stochastic differential equations.

Suggested Citation

  • Xuchen Wu & Sebastian Jaimungal, 2024. "Broker-Trader Partial Information Nash Equilibria," Papers 2412.17712, arXiv.org.
    • Handle: RePEc:arx:papers:2412.17712
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    References listed on IDEAS

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    1. Álvaro Cartea & Yixuan Wang, 2020. "Market Making With Alpha Signals," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 23(03), pages 1-26, May.
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    3. 'Alvaro Cartea & Sebastian Jaimungal & Leandro S'anchez-Betancourt, 2024. "Nash Equilibrium between Brokers and Traders," Papers 2407.10561, arXiv.org, revised Jul 2024.
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    8. Alexander Barzykin & Robert Boyce & Eyal Neuman, 2024. "Unwinding Toxic Flow with Partial Information," Papers 2407.04510, arXiv.org.
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