Proportional Clearing Mechanisms in Financial Systems : An Axiomatic Approach

We address the problem of clearing mutual obligations among agents when a financial network collapses. To do so, we adopt an axiomatic approach and provide the first comprehensive characterization of the rules based on the principle of proportionality, covering the entire domain of financial systems. While a previous attempt by Cs\'{o}ka and Herings (2021) tackled this issue in a context where agents have strictly positive initial endowments, we show that their properties do not fully capture the set of proportional rules when extended to the full financial systems domain.To overcome this limitation, we introduce new properties that emphasize the value of equity of the firms in the network. We show that a clearing mechanism satisfies compatibility, limited liability, absolute priority, equity continuity, and non-manipulability by clones if and only if each agent receives a payment proportional to the value of their claims. This characterization holds in the framework studied by Cs\'{o}ka and Herings (2021)