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arXiv · 2403.16232

Mean Field Game of Mutual Holding with common noise

Leila Bassou·Mao Fabrice Djete·Nizar Touzi
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Abstract

We consider the mean field game of cross--holding introduced in \citeauthor*{DjeteTouzi} \cite{DjeteTouzi} in the context where the equity value dynamics are affected by a common noise. In contrast with \cite{DjeteTouzi}, 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.

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Leila Bassou, Mao Fabrice Djete, Nizar Touzi. 2024-03-24. Mean Field Game of Mutual Holding with common noise. https://arxiv.org/abs/2403.16232

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