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Dynamic Debt Swapping in Financial Networks

Authors Henri Froese, Martin Hoefer , Lisa Wilhelmi

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  • Theory of computation → Theory and algorithms for application domains
  • Networks → Network algorithms
Keywords
  • Debt Swap
  • Financial Networks
  • Local Search

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Abstract

A debt swap is an elementary edge swap in a directed, weighted graph, where two edges with the same weight swap their targets. Debt swaps are a natural and appealing operation in financial networks, in which nodes are banks and edges represent debt contracts. They can improve the clearing payments and the stability of these networks. However, their algorithmic properties are not well-understood.
We analyze the computational complexity of debt swapping. Our main interest lies in semi-positive swaps, in which no creditor strictly suffers and at least one strictly profits. These swaps lead to a Pareto-improvement in the entire network. We consider network optimization via sequences of v-improving debt swaps from which a given bank v strictly profits. For ranking-based clearing, we show that every sequence of semi-positive v-improving swaps has polynomial length. In contrast, for arbitrary v-improving swaps, the problem of reaching a network configuration that allows no further swaps is PLS-complete. We identify cases in which short sequences of semi-positive swaps exist even without the v-improving property.

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Henri Froese, Martin Hoefer, and Lisa Wilhelmi. Dynamic Debt Swapping in Financial Networks. In 4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 330, pp. 2:1-2:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.SAND.2025.2

Author Details

Henri Froese
  • Goethe University Frankfurt, Germany
Martin Hoefer
  • RWTH Aachen University, Germany
Lisa Wilhelmi
  • RWTH Aachen University, Germany

Funding

  • Hoefer, Martin: Supported by DFG Research Unit ADYN under grant DFG 411362735 and ATHENE National Research Center for Applied Cybersecurity.
  • Wilhelmi, Lisa: Supported by DFG Research Unit ADYN under grant DFG 411362735.

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