Optimization of Fire Sales and Borrowing in Systemic Risk

TL;DR

This paper develops a comprehensive framework for modeling systemic financial risk, incorporating fire sales, price impacts, and borrowing options, and establishes conditions for the existence and uniqueness of solutions.

Contribution

It introduces a novel model that includes both uncollateralized and collateralized borrowing, and characterizes clearing solutions as Nash equilibria in an aggregation game.

Findings

Provided sufficient conditions for existence of clearing solutions

Proved uniqueness of solutions under certain conditions

Linked clearing solutions to Nash equilibria in a financial network

Abstract

This paper provides a framework for modeling financial contagion in a network subject to fire sales and price impacts, but allowing for firms to borrow to cover their shortfall as well. We consider both uncollateralized and collateralized loans. The main results of this work are providing sufficient conditions for existence and uniqueness of the clearing solutions (i.e., payments, liquidations, and borrowing); in such a setting any clearing solution is the Nash equilibrium of an aggregation game.