4 Search Results for "Schuldenzucker, Steffen"

Document
DOI: 10.4230/LIPIcs.STACS.2026.14
Computing Tarski Fixed Points in Financial Networks

Authors: Leander Besting, Martin Hoefer, and Lars Huth

Published in: LIPIcs, Volume 364, 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)

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

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)

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@InProceedings{besting_et_al:LIPIcs.STACS.2026.14,
  author =	{Besting, Leander and Hoefer, Martin and Huth, Lars},
  title =	{{Computing Tarski Fixed Points in Financial Networks}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{14:1--14:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-412-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{364},
  editor =	{Mahajan, Meena and Manea, Florin and McIver, Annabelle and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2026.14},
  URN =		{urn:nbn:de:0030-drops-255038},
  doi =		{10.4230/LIPIcs.STACS.2026.14},
  annote =	{Keywords: Tarski Fixed Points, Financial Networks, Minimal Clearing, Claims Trade}
}
Document
DOI: 10.4230/LIPIcs.SAND.2025.2
Dynamic Debt Swapping in Financial Networks

Authors: Henri Froese, Martin Hoefer, and Lisa Wilhelmi

Published in: LIPIcs, Volume 330, 4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025)

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.
Cite as

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)

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@InProceedings{froese_et_al:LIPIcs.SAND.2025.2,
  author =	{Froese, Henri and Hoefer, Martin and Wilhelmi, Lisa},
  title =	{{Dynamic Debt Swapping in Financial Networks}},
  booktitle =	{4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025)},
  pages =	{2:1--2:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-368-3},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{330},
  editor =	{Meeks, Kitty and Scheideler, Christian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2025.2},
  URN =		{urn:nbn:de:0030-drops-230550},
  doi =		{10.4230/LIPIcs.SAND.2025.2},
  annote =	{Keywords: Debt Swap, Financial Networks, Local Search}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2020.46
Strategic Payments in Financial Networks

Authors: Nils Bertschinger, Martin Hoefer, and Daniel Schmand

Published in: LIPIcs, Volume 151, 11th Innovations in Theoretical Computer Science Conference (ITCS 2020)

Abstract
In their seminal work on systemic risk in financial markets, Eisenberg and Noe [Larry Eisenberg and Thomas Noe, 2001] proposed and studied a model with n firms embedded into a network of debt relations. We analyze this model from a game-theoretic point of view. Every firm is a rational agent in a directed graph that has an incentive to allocate payments in order to clear as much of its debt as possible. Each edge is weighted and describes a liability between the firms. We consider several variants of the game that differ in the permissible payment strategies. We study the existence and computational complexity of pure Nash and strong equilibria, and we provide bounds on the (strong) prices of anarchy and stability for a natural notion of social welfare. Our results highlight the power of financial regulation - if payments of insolvent firms can be centrally assigned, a socially optimal strong equilibrium can be found in polynomial time. In contrast, worst-case strong equilibria can be a factor of Ω(n) away from optimal, and, in general, computing a best response is an NP-hard problem. For less permissible sets of strategies, we show that pure equilibria might not exist, and deciding their existence as well as computing them if they exist constitute NP-hard problems.
Cite as

Nils Bertschinger, Martin Hoefer, and Daniel Schmand. Strategic Payments in Financial Networks. In 11th Innovations in Theoretical Computer Science Conference (ITCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 151, pp. 46:1-46:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{bertschinger_et_al:LIPIcs.ITCS.2020.46,
  author =	{Bertschinger, Nils and Hoefer, Martin and Schmand, Daniel},
  title =	{{Strategic Payments in Financial Networks}},
  booktitle =	{11th Innovations in Theoretical Computer Science Conference (ITCS 2020)},
  pages =	{46:1--46:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-134-4},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{151},
  editor =	{Vidick, Thomas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2020.46},
  URN =		{urn:nbn:de:0030-drops-117316},
  doi =		{10.4230/LIPIcs.ITCS.2020.46},
  annote =	{Keywords: Nash Equilibrium, Financial Network, Systemic Risk, Price of Anarchy, Equilibrium Computation}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2017.32
Finding Clearing Payments in Financial Networks with Credit Default Swaps is PPAD-complete

Authors: Steffen Schuldenzucker, Sven Seuken, and Stefano Battiston

Published in: LIPIcs, Volume 67, 8th Innovations in Theoretical Computer Science Conference (ITCS 2017)

Abstract
We consider the problem of clearing a system of interconnected banks that have been exposed to a shock on their assets. Eisenberg and Noe (2001) showed that when banks can only enter into simple debt contracts with each other, then a clearing vector of payments can be computed in polynomial time. In this paper, we show that the situation changes radically when banks can also enter into credit default swaps (CDSs), i.e., financial derivative contracts that depend on the default of another bank. We prove that computing an approximate solution to the clearing problem with sufficiently small constant error is PPAD-complete. To do this, we demonstrate how financial networks with debt and CDSs can encode arithmetic operations such as addition and multiplication. Our results have practical impact for network stress tests and reveal computational complexity as a new concern regarding the stability of the financial system.
Cite as

Steffen Schuldenzucker, Sven Seuken, and Stefano Battiston. Finding Clearing Payments in Financial Networks with Credit Default Swaps is PPAD-complete. In 8th Innovations in Theoretical Computer Science Conference (ITCS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 67, pp. 32:1-32:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{schuldenzucker_et_al:LIPIcs.ITCS.2017.32,
  author =	{Schuldenzucker, Steffen and Seuken, Sven and Battiston, Stefano},
  title =	{{Finding Clearing Payments in Financial Networks with Credit Default Swaps is PPAD-complete}},
  booktitle =	{8th Innovations in Theoretical Computer Science Conference (ITCS 2017)},
  pages =	{32:1--32:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-029-3},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{67},
  editor =	{Papadimitriou, Christos H.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2017.32},
  URN =		{urn:nbn:de:0030-drops-81558},
  doi =		{10.4230/LIPIcs.ITCS.2017.32},
  annote =	{Keywords: Financial Networks, Credit Default Swaps, Clearing Systems, Arithmetic Circuits, PPAD}
}
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