Optimization of Fire Sales and Borrowing in Systemic Risk

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 the 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.