{getToc} $title={Table of Contents}
Summary
The paper studies a Nash equilibrium between a broker and an informed trader in a partial information setting. The broker observes only the prices of assets in the lit market, while the informed trader has access to a private trading signal. The authors characterize the equilibrium and prove its existence and uniqueness in a small time regime.
Highlights
- The broker's performance criterion is strictly concave in their trading strategy.
- The informed trader's performance criterion is strictly concave in their trading strategy.
- The broker's optimal trading strategy involves filtering the informed trader's signal.
- The informed trader's optimal trading strategy involves maximizing their expected wealth.
- The Nash equilibrium is characterized by a system of forward-backward stochastic differential equations (FBSDEs).
- The FBSDEs are solved using a contraction mapping argument.
- The solution to the FBSDEs provides the optimal trading strategies for the broker and the informed trader.
Key Insights
- The paper provides a novel framework for analyzing the strategic interaction between a broker and an informed trader in a partial information setting. This framework can be used to study other problems in finance that involve asymmetric information.
- The characterization of the Nash equilibrium in terms of FBSDEs provides a powerful tool for solving complex problems in finance. FBSDEs have been used to study a wide range of problems in finance, including optimal portfolio selection and risk management.
- The paper highlights the importance of filtering in finance. The broker's optimal trading strategy involves filtering the informed trader's signal, which is a key insight that can be applied to other problems in finance.
- The paper provides a new perspective on the role of information in finance. The informed trader's private signal is a key driver of the Nash equilibrium, and the paper shows how the broker's optimal trading strategy depends on their ability to filter this signal.
- The paper has implications for the regulation of financial markets. The Nash equilibrium characterized in the paper can be used to study the impact of different regulatory regimes on the behavior of brokers and informed traders.
- The paper provides a new framework for analyzing the impact of high-frequency trading on financial markets. The Nash equilibrium characterized in the paper can be used to study the impact of high-frequency trading on the behavior of brokers and informed traders.
- The paper highlights the importance of stochastic control theory in finance. The characterization of the Nash equilibrium in terms of FBSDEs relies on stochastic control theory, which is a key tool for solving complex problems in finance.
Mindmap
Citation
Wu, X., & Jaimungal, S. (2024). Broker-Trader Partial Information Nash Equilibria (Version 1). arXiv. https://doi.org/10.48550/ARXIV.2412.17712