A Continuous-Time Model of Financial Clearing
42 Pages Posted: 31 Jul 2020 Last revised: 14 Sep 2020
Date Written: September 4, 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 use the machinery of Markov chains 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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