A Continuous-Time Model of Financial Clearing
43 Pages Posted: 31 Jul 2020 Last revised: 18 Dec 2020
Date Written: December 9, 2020
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.
Keywords: Financial networks, clearing vector, continuous time, quasi-linear optimization
JEL Classification: G21, G33, C61
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