We present a simple continuous-time model of clearing in financial networks. Financial firms are represented as “tanks” filled with fluid (money), flowing in and out. Once the “pipes” connecting the “tanks” are open, the system reaches the clearing payment vector in finite time. This approach provides a simple recursive solution to a classical static model of financial clearing in bankruptcy, and suggests a practical payment mechanism. With sufficient resources, a system of mutual obligations can be restructured into an equivalent system that has a cascade structure: there is a group of banks that paid off their debts, another group that owes money only to banks in the first group, and so on. We demonstrate that the machinery of Markov chains provides a powerful method to analyze evolution of a deterministic dynamical system.

More on this topic

BFI Working Paper·Jun 30, 2025

Building Costs and House Prices

Brian Potter and Chad Syverson
Topics: Financial Markets
BFI Working Paper·Jun 23, 2025

Macro Shocks and Firm-Level Response Heterogeneity

Steven J. Davis, Stephen Hansen, and Cristhian Seminario-Amez
Topics: Financial Markets
BFI Working Paper·Apr 7, 2025

Non-User Utility and Market Power: The Case of Smartphones

Leonardo Bursztyn, Rafael Jiménez-Durán, Aaron Leonard, Filip Milojević, and Christopher Roth
Topics: Financial Markets