Mean Field Game of Mutual Holding with common noise (2403.16232v1)
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.
- H. Brézis. Analyse fonctionnelle: théorie et applications. Collection Mathématiques appliquées pour la maîtrise. Dunod, 1999. ISBN 9782100043149.
- P. Briand and Y. Hu. Quadratic BSDEs with convex generators and unbounded terminal conditions. Probability Theory and Related Fields, 141(3-4):543–567, 2008.
- Utility maximization in incomplete markets with random endowment. Finance and Stochastics, 5(2):259–272, 2001.
- M. F. Djete and N. Touzi. Mean field game of mutual holding. arXiv preprint arXiv:2104.03884, 2022.
- Mean field game of mutual holding with defaultable agents, and systemic risk. arXiv preprint arXiv:2303.07996, 2023.
- C. Fontana. Weak and strong no–arbitrage conditions for continuous financial markets. International Journal of Theoretical and Applied Finance, 18(01):1550005, 2015. doi: 10.1142/S0219024915500053. URL https://doi.org/10.1142/S0219024915500053.
- Bond pricing and the term structure of interest rates: A new methodology for contingent claims valuation. Econometrica: Journal of the Econometric Society, pages 77–105, 1992.
- J. Hugonnier and D. Kramkov. Optimal investment with random endowments in incomplete markets. The Annals of Applied Probability, 14(2):845–864, 2004.
- I. Karatzas and G. Zitković. Optimal consumption from investment and random endowment in incomplete semimartingale markets. The Annals of Applied Probability, 31(4):1821–1858, 2003.
- T. Kato. Perturbation theory for linear operators. Classics in mathematics. Springer, 1980.
- O. Mostovyi. Optimal investment with intermediate consumption and random endowment. Mathematical Finance, 27(1):96–114, 2017.
- J.-A. Yan. Caractérisation d’une classe d’ensembles convexes de l1superscript𝑙1l^{1}italic_l start_POSTSUPERSCRIPT 1 end_POSTSUPERSCRIPT ou h1superscriptℎ1h^{1}italic_h start_POSTSUPERSCRIPT 1 end_POSTSUPERSCRIPT. Séminaire de probabilités de Strasbourg, 14:220–222, 1980. URL http://www.numdam.org/item/SPS_1980__14__220_0/.
- G. Zitković. Utility maximization with a stochastic clock and an unbounded random endowment. The Annals of Applied Probability, 15(1B):748–777, 2005.
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