English

Mean Field Game of Mutual Holding with common noise

Probability 2024-03-26 v1 Optimization and Control

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.

Keywords

Cite

@article{arxiv.2403.16232,
  title  = {Mean Field Game of Mutual Holding with common noise},
  author = {Leila Bassou and Mao Fabrice Djete and Nizar Touzi},
  journal= {arXiv preprint arXiv:2403.16232},
  year   = {2024}
}