Public Academic Lecture: Clearing in Financial Networks

Public Academic Lecture Series

Abstract: Clearing of financial system, i.e. of a network of interconnecting banks, is a procedure of simultaneous repaying debts to reduce their total volume. The vector whose components are repayments of each bank is called clearing vector. In simple models considered by Eisenberg and Noe (2001) and, independently, by Suzuki (2002), it was shown that the clearing to the minimal value of debts accordingly to natural rules can be formulated as a fixpoint problem. The existence of their solutions, i.e. of clearing vectors, is rather straightforward and can be obtained by a direct reference to the Knaster–Tarski or Brouwer theorems. 

The uniqueness of clearing vectors is a more delicate problem which was solved by Eisenberg and Noe using a graph structure of the financial network. We discuss the modern state of art of the theory and, in particular, algorithmic aspects of solving clearing equations in relations with those arising in the theory of optimal stopping.