Mean Field Games with Common Noise: Modeling Systemic Financial Decarbonization

Mean Field Games (MFG) theory, introduced by J.-M. Lasry and P.-L. Lions in 2006, offers a powerful analytical framework for modeling strategic interactions among a continuum of rational agents. Inspired by mean field techniques in statistical physics, MFG theory distinguishes itself by capturing the behavior of decision-makers who optimize individual objectives in response to the evolving collective state. Recent developments have extended MFG models into the realm of green finance, particularly in analyzing the strategic behavior of firms and investors under climate-related risks. A notable contribution in this area is the work of P. Tankov and P. Lavigne (2023), “Decarbonization of Financial Markets: A Mean-Field Game Approach”, which introduces a rigorous MFG framework for modeling decarbonization dynamics in financial markets. Their model establishes the existence and uniqueness of an optimal stochastic discount factor, offering significant insights into the pricing of assets and the decarbonization dynamics in the presence of climate risk. This thesis provides an accessible introduction to the foundational concepts of Mean Field Games theory, presents a detailed exposition and proof of the main results from Tankov and Lavigne’s model, and provides a qualitative discussion of the simulation outcomes.