DP15117 A Continuous-Time Model of Financial Clearing
|Author(s):||Konstantin Sonin, Isaac Sonin|
|Publication Date:||July 2020|
|Date Revised:||November 2020|
|Keyword(s):||clearing vector, continuous time, Financial Networks, Markov chains|
|Programme Areas:||Public Economics, Financial Economics|
|Link to this Page:||cepr.org/active/publications/discussion_papers/dp.php?dpno=15117|
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 how the machinery of Markov chains can be used to analyze evolution of a deterministic dynamical system.