Mean Field Game of Mutual Cross-Holding
Modeling diversification strategies in financial networks using mean field game theory
Project Overview
This project explores the dynamics of mutual cross-holding situations in financial markets through the lens of mean field game theory. Cross-holding occurs when companies hold shares in each other, creating complex interdependencies in financial networks.
Using discrete-time mean field games, we modeled how rational agents (shareholders) make optimal decisions regarding their diversification strategies while considering the aggregate behavior of the entire market.
Our study was limited to a single time step, but it is quite sufficient to illustrate the main ideas of what we needed to show. Moreover, this project is meant to be scaled and extended to multiple time steps, and should be extended to continuous time.
Methodology
- Mean Field Game Framework: Formulated the problem as a discrete-time MFG where each agent optimizes their portfolio while accounting for the empirical distribution of all agents' holdings.
- Established the mean field game problem : Defined the problem when the number of agents is large. Defined what we meant by solution to the problem.
- Solved the mean field game problem Determined the Nash Equilibrium of the game and approximated the finite number of agents solution.
- Numerical Simulations: Implemented python simulations on various hypothesis on the idiosyncratic risk of the agents. We chose a Ornstein-Uhlenbeck model for the idiosynchratic risk.
- Risk Analysis: Evaluated how the distribution of the possible values of the agents shares varied with and without cross-holding. We observed that the variance of the shares was reduced when cross-holding was present.