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Computing Tarski Fixed Points in Financial Networks

Authors Leander Besting , Martin Hoefer , Lars Huth

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LIPIcs.STACS.2026.14.pdf
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Subject Classification

ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
  • Networks → Network algorithms
Keywords
  • Tarski Fixed Points
  • Financial Networks
  • Minimal Clearing
  • Claims Trade

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Abstract

Modern financial networks are highly connected and result in complex interdependencies of the involved institutions. In the prominent Eisenberg-Noe model [Eisenberg and Noe, 2001], a fundamental aspect is clearing - to determine the amount of assets available to each financial institution in the presence of potential defaults and bankruptcy. A clearing state represents a fixed point that satisfies a set of natural axioms. Existence can be established (even in broad generalizations of the model) using Tarski’s theorem. While a maximal fixed point can be computed in polynomial time, the complexity of computing other fixed points is open. In this paper, we provide an efficient algorithm to compute a minimal fixed point. Our algorithm applies in a broad generalization of the Eisenberg-Noe model with any monotone, piecewise-linear payment functions and default costs. We also study claims trading, a local network adjustment to improve clearing, when networks are evaluated with minimal clearing. We provide an efficient algorithm to decide existence of Pareto-improving trades and compute optimal ones if they exist.

Cite As Get BibTex

Leander Besting, Martin Hoefer, and Lars Huth. Computing Tarski Fixed Points in Financial Networks. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 14:1-14:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.STACS.2026.14

Author Details

Leander Besting
  • Department of Computer Science, RWTH Aachen University, Germany
Martin Hoefer
  • Department of Computer Science, RWTH Aachen University, Germany
Lars Huth
  • Department of Computer Science, RWTH Aachen University, Germany

Funding

This work was supported by DFG Research Unit ADYN (project number 411362735) and grant DFG Ho 3831/9-1 (project number 514505843).

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