Optimal hedging of an informed broker facing many traders
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.
Keywords
Cite
@article{arxiv.2506.08992,
title = {Optimal hedging of an informed broker facing many traders},
author = {Philippe Bergault and Pierre Cardaliaguet and Wenbin Yan},
journal= {arXiv preprint arXiv:2506.08992},
year = {2025}
}