Financial networks with singleton liability priorities

Abstract

Financial networks model debt obligations between economic firms. Computational and game-theoretic analyses of these networks have been recent focus of the literature. The main computational challenge in this context is the clearing problem, a fixed point search problem that essentially determines insolvent firms and their exposure to systemic risk, technically known as recovery rates. When Credit Default Swaps, a derivative connected to the 2008 financial crisis, are factored into the obligations, the clearing problem becomes more complex. Specifically, whenever insolvent firms pay their debts proportionally to their recovery rates, computing a weakly approximate solution was shown by Schuldenzucker et al. (2017) to be PPAD-complete. Additionally, Ioannidis et al. (2022) showed that computing a strongly approximate solution in the same framework is FIXP-complete.This paper addresses the computational complexity of the clearing problem in financial networks with derivatives, whenever payment priorities among creditors are applied. This practically relevant model has only been studied from a game-theoretic standpoint. We explicitly study the clearing problem whenever the firms pay according to a singleton liability priority list and prove that it is FIXP-complete. Finally, we provide a number of NP-hardness results for the computation of priority lists that optimise specific objectives of importance in the domain.