Proportional clearing mechanisms in financial systems: an axiomatic approach

When a financial network collapses, how should mutual obligations among all agents be cleared? We study this problem taking an axiomatic approach and provide the first characterization of the family of rules based on the principle of proportionality in the entire domain of financial systems. A previous attempt to address this issue was done by Csóka and Herings (2021), but in a tight context where all agents dispose of strictly positive initial endowments. We show that their properties, when accommodated to the full domain of financial systems, no longer characterize the set of proportional rules. To overcome this drawback, we formulate new properties emphasizing the value of equity of the firms in the network. In particular, we show that a clearing mechanism satisfies compatilibity, limited liability, absolute priority, equity continuity, and non-manipulability by clones if and only if each agent is paid proportionally to the value of its claims. Remarkably, our result also holds in the framework studied by Csóka and Herings (2021).