Optimal hedging of an informed broker facing many traders

TL;DR

This paper develops a theoretical framework using mean-field game theory to analyze the optimal hedging strategies of an informed broker interacting with many traders, revealing equilibrium behaviors and convergence properties.

Contribution

It introduces a novel mean-field game model for an informed broker with exclusive information, deriving equilibrium strategies and analyzing the large-trader limit.

Findings

Derives equilibrium strategies for broker and traders

Shows convergence of finite-player models to mean-field limit

Identifies Stackelberg equilibrium in the market setting

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.