Algorithms for Claims Trading

ACM Transactions on Computation Theory, vol. 18, pp. 1–31

Abstract

Understanding and mitigating systemic risk is an important ongoing challenge in financial networks. We study an approach to rescue a bank in distress based on the idea of claims trading , a notion defined in Chapter 11 of the U.S. Bankruptcy Code. We formalize the idea in the context of the seminal model of financial networks by Eisenberg and Noe [ 9 ]. Given two banks v and w , we consider the operation that w takes over some claims of v and in return gives liquidity to v (or creditors of v ) to ultimately rescue v (or mitigate contagion effects). We study structural properties and computational complexity of decision and optimization problems arising from this trading operation. When trading claims for which v is the creditor, we show that there is no trade in which both banks v and w strictly improve their assets. While deciding the existence of a trade, in which v profits strictly and w remains indifferent, can be NP -hard, we provide FPTAS’es to approximate such a trade, even when banks settle their debt using general monotone payment functions. When trading claims with a common debtor, we show positive and negative results that crucially depend on the payment functions.

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