Computing Tarski Fixed Points in Financial Networks
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866911454344511488 |
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| author | Besting, Leander Hoefer, Martin Huth, Lars |
| author_facet | Besting, Leander Hoefer, Martin Huth, Lars |
| contents | Modern financial networks are highly connected and result in complex interdependencies of the involved institutions. In the prominent Eisenberg-Noe model, 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 that runs in strongly polynomial time. It applies in a broad generalization of the Eisenberg-Noe model with any monotone, piecewise-linear payment functions and default costs. Moreover, in this scenario we provide a polynomial-time algorithm to compute a maximal fixed point. For networks without default costs, we can efficiently decide the existence of fixed points in a given range.
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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_16387 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Computing Tarski Fixed Points in Financial Networks Besting, Leander Hoefer, Martin Huth, Lars Data Structures and Algorithms Computer Science and Game Theory Risk Management Modern financial networks are highly connected and result in complex interdependencies of the involved institutions. In the prominent Eisenberg-Noe model, 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 that runs in strongly polynomial time. It applies in a broad generalization of the Eisenberg-Noe model with any monotone, piecewise-linear payment functions and default costs. Moreover, in this scenario we provide a polynomial-time algorithm to compute a maximal fixed point. For networks without default costs, we can efficiently decide the existence of fixed points in a given range. 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. |
| title | Computing Tarski Fixed Points in Financial Networks |
| topic | Data Structures and Algorithms Computer Science and Game Theory Risk Management |
| url | https://arxiv.org/abs/2602.16387 |