Uniqueness of Clearing Payment Matrices in Financial Networks

We study bankruptcy problems in financial networks the presence of general laws. The set clearing payment matrices is shown to be a lattice, which guarantees existence greatest and least payment. Multiplicity both theoretical practical concern. present new condition for uniqueness that generalizes all existing conditions proposed literature. Our depends on decomposition network into strongly connected components. A component contains more than one agent called cycle involved agents are cyclical agents. If there without successors, then such should have positive endowment. division rule used by with endowment monotonic zero strictly monotonic. Since rules involving priorities not monotonic, matrix much bigger concern proportional ones. also show how related continuity rules.