Hierarchical modeling of systemic risk via mean field games
Rathod, Prathmesh
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https://hdl.handle.net/2142/129631
Description
Title
Hierarchical modeling of systemic risk via mean field games
Author(s)
Rathod, Prathmesh
Issue Date
2025-05-08
Director of Research (if dissertation) or Advisor (if thesis)
Dayanikli , Gokce
Department of Study
Industrial&Enterprise Sys Eng
Discipline
Industrial Engineering
Degree Granting Institution
University of Illinois Urbana-Champaign
Degree Name
M.S.
Degree Level
Thesis
Keyword(s)
Mean Field Games, Game Theory, Systemic Risk, Optimization
Abstract
In the aftermath of the 2008 global financial crisis, the question of how to manage and mitigate the systemic risk in the banking sector has become a cornerstone of financial regulation objectives and policy. Motivated by this observation, this thesis aims to model the mitigation of cascading systemic risk at the local bank level by introducing the policies of the central banks and International Monetary Fund (IMF) into the modeling. Specifically, we introduce a mathematical model in which local banks in K many countries, their central banks, the IMF is modeled in a game theoretical setup. In order to model the game problem among large number of local banks in each country, we use the mean field game (MFG) methodology. We accomplish this by extending the model of Carmona, Fouque, and Sun [1] to the case where we can accommodate multiple populations that represent different countries. Therefore, we first give the mathematical model of the local banks, define the multi-population MFG Nash equilibrium for them, and present the theoretical characterization results by using Pontryagin maximum principle given the policies of the central bank and the IMF. Later, we introduce the mathematical model of the central banks and we present the Nash equilibrium definition between the central banks and local banks. We conclude by introducing the characterization result for the Nash equilibrium between central banks and local banks by using forward backward stochastic differential equations. Finally, we introduce the model of IMF and define the Stackelberg equilibrium in the whole system where IMF sets country specific policies and optimize these policies by taking into account the Nash equilibrium response of the central and local banks in each country.
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