2025/01/21 by Leonardo Stella, Dario Bauso, Stella, Leonardo +5
Economics, Econometrics and Finance · Physics and Astronomy · #Complex Systems and Time Series Analysis #Dynamical Systems (math.DS) #FOS: Electrical engineering #FOS: Mathematics #Opinion Dynamics and Social Influence #Optimization and Control (math.OC) #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2501.12156
openalex publication_date 2025/01/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
Cascading failures, such as bankruptcies and defaults, pose a serious threat for the resilience of the global financial system. Indeed, because of the complex investment and cross-holding relations within the system, failures can occur as a result of the propagation of a financial collapse from one organization to another. While this problem has been studied in depth from a static angle, namely, when the system is at an equilibrium, we take a different perspective and study the corresponding dynamical system. The contribution of this paper is threefold. First, we carry out a systematic analysis of the regions of attraction and invariance of the system orthants, defined by the positive and negative values of the organizations' equity. Second, we investigate periodic solutions and show through a counterexample that there could exist periodic solutions of period greater than 2. Finally, we study the problem of finding the smallest cash injection that would bring the system to the maximal invariant region of the positive orthant.