# Mean Field Game of Mutual Holding with common noise

arXiv: https://arxiv.org/abs/2403.16232 · HTML: https://mlsanity.com/paper/2403.16232/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Mar 2024.

## Built on by (most cited first, 1 of 1)

- [Population-Aware Imitation Learning in Mean-field Games with Common Noise](https://mlsanity.com/paper/2605.03357/) (2026)

## Abstract (arXiv)

We consider the mean field game of cross--holding introduced in citeauthor*DjeteTouzi citeDjeteTouzi in the context where the equity value dynamics are affected by a common noise. In contrast with citeDjeteTouzi, the problem exhibits the standard paradigm of mean--variance trade off. Our crucial observation is to search for equilibrium solutions of our mean field game among those models which satisfy an appropriate notion of no--arbitrage. Under this condition, it follows that the representative agent optimization step is reduced to a standard portfolio optimization problem with random endowment.