Mean field game of mutual holding with defaultable agents, and systemic risk

Mao Fabrice Djete, Gaoyue Guo () and Nizar Touzi
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Mao Fabrice Djete: CMAP - Centre de Mathématiques Appliquées de l'Ecole polytechnique - Inria - Institut National de Recherche en Informatique et en Automatique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique
Gaoyue Guo: MICS - Mathématiques et Informatique pour la Complexité et les Systèmes - CentraleSupélec - Université Paris-Saclay, Fédération de Mathématiques de CentraleSupélec - CentraleSupélec - Université Paris-Saclay - CNRS - Centre National de la Recherche Scientifique
Nizar Touzi: CMAP - Centre de Mathématiques Appliquées de l'Ecole polytechnique - Inria - Institut National de Recherche en Informatique et en Automatique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique

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Abstract: We introduce the possibility of default in the mean field game of mutual holding of Djete and Touzi [11]. This is modeled by introducing absorption at the origin of the equity process. We provide an explicit solution of this mean field game. Moreover, we provide a particle system approximation, and we derive an autonomous equation for the time evolution of the default probability, or equivalently the law of the hitting time of the origin by the equity process. The systemic risk is thus described by the evolution of the default probability.

Date: 2023
Note: View the original document on HAL open archive server: https://hal.science/hal-04565544v1
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Published in SIAM Journal on Control and Optimization, 2023, 64 (1), pp.24-58. ⟨10.1137/24M1658668⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-04565544

DOI: 10.1137/24M1658668

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