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Optimal hedging of an informed broker facing many traders

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  • Philippe Bergault
  • Pierre Cardaliaguet
  • Wenbin Yan

Abstract

This paper investigates the optimal hedging strategies of an informed broker interacting with multiple traders in a financial market. We develop a theoretical framework in which the broker, possessing exclusive information about the drift of the asset's price, engages with traders whose trading activities impact the market price. Using a mean-field game approach, we derive the equilibrium strategies for both the broker and the traders, illustrating the intricate dynamics of their interactions. The broker's optimal strategy involves a Stackelberg equilibrium, where the broker leads and the traders follow. Our analysis also addresses the mean field limit of finite-player models and shows the convergence to the mean-field solution as the number of traders becomes large.

Suggested Citation

  • Philippe Bergault & Pierre Cardaliaguet & Wenbin Yan, 2025. "Optimal hedging of an informed broker facing many traders," Papers 2506.08992, arXiv.org.
    • Handle: RePEc:arx:papers:2506.08992
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    References listed on IDEAS

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    3. Philippe Bergault & Leandro S'anchez-Betancourt, 2024. "A Mean Field Game between Informed Traders and a Broker," Papers 2401.05257, arXiv.org.
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