Banks as Tanks: A Continuous-Time Model of Financial Clearing

TL;DR

This paper introduces a continuous-time dynamical model for financial clearing in networks, using fluid flow analogy to analyze and solve static bankruptcy models with practical payment mechanisms.

Contribution

It proposes a novel continuous-time framework for financial clearing, providing recursive solutions and restructuring mutual obligations into cascade systems.

Findings

Finite-time convergence to clearing payment vectors

Restructuring of mutual obligations into cascade structures

Application of Markov chains to analyze system evolution

Abstract

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 "pipes" connecting "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. Technically, we use the machinery of Markov chains to analyze evolution of a deterministic dynamical system.