Stefano Marmi (Scuola Normale Superiore Pisa) and Matteo Tanzi (King's College London)

Abstract: Well established economic and financial models provide valuable insights but many real-world phenomena, such as persistent commodity cycles and systemic financial crises, exhibit complex dynamics that challenge standard equilibrium frameworks. Moreover, market “imperfections,” like limited liquidity and regulatory impacts during stress, can lead to non-linear deterministic behavior. Noise can also be related to different time scales (and delays) between market data and agents’ portfolio allocation decisions. This seminar will review some case studies and explore how dynamical systems and ergodic theory offer tools and conceptual frameworks for understanding these complexities.

Abstract: Systemic financial risk refers to the simultaneous failure or destabilization of multiple financial institutions, often triggered by contagion mechanisms or common exposures to shocks. This talk presents a dynamical model of bank leverage—the ratio of asset holdings to equity—a quantity that both reflects and drives risk dynamics. We model how banks, constrained by Value-at-Risk (VaR) regulations, adjust their leverage in response to changes in the price of a single asset, assumed to be held in fixed proportion across banks. This leverage-targeting behavior introduces a procyclical feedback loop between asset prices and leverage. In the dynamics, this can manifest as logistic-like behavior with a rich bifurcation structure across model parameters. By analyzing these coupled dynamics in both isolated and interconnected bank models, we outline a framework for understanding how systemic risk can emerge from seemingly rational micro-level behavior.