Optimal hedging of an informed broker facing many traders

2025-06-10

AI Summary

This paper investigates the optimal hedging strategy of an informationally advantaged market maker—who observes the true asset drift—in a multi-trader market. Focusing on price-impact-seeking traders, it formulates a Stackelberg hierarchical game: the market maker acts as leader, while traders are followers. Innovatively, it embeds the Stackelberg equilibrium within a mean-field game framework and rigorously establishes the large-population convergence of the finite-player model to the mean-field solution, with convergence rate (O(1/N)). Using stochastic optimal control and asymptotic analysis, the paper derives closed-form expressions for equilibrium strategies and quantifies the hedging performance gain attributable to informational advantage. The results reveal endogenous market stratification under asymmetric information and provide both theoretical foundations and computationally tractable tools for high-frequency market making and information-sensitive risk management.

Technology Category

• Game Theory and Economic Paradigms: Imperfect Information
• Multiagent Systems: Mechanism Design
• Search and Optimization: Adversarial Search

Application Category

• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions
• Security and Privacy: Large-scale security measurements
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

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.

Problem

• Optimal hedging strategies for an informed broker
• Interactions between broker and multiple traders
• Mean-field game approach for equilibrium strategies

Innovation

• Stackelberg equilibrium for broker strategy
• Mean-field game approach for interactions
• Convergence analysis in mean-field limit