Lars Huth | Searcharxiv

arXiv2026

Computing Tarski Fixed Points in Financial Networks

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.

cs.DS↗

arXiv2025

Fractional Claims Trades and Donations in Financial Networks

Exploring measures to improve financial networks and mitigate systemic risks is an ongoing challenge. We study claims trading, a notion defined in Chapter 11 of the U.S. Bankruptcy Code. For a bank $v$ in distress and a trading partner $w$, the latter is taking over some claims of $v$ and in return giving liquidity to $v$. The idea is to rescue $v$ (or mitigate contagion effects from $v$'s insolvency). We focus on the impact of trading claims fractionally, when $v$ and $w$ can agree to trade only part of a claim. In addition, we study donations, in which $w$ only provides liquidity to $v$. They can be seen as special claims trades. When trading a single claim or making a single donation in networks without default cost, we show that it is impossible to strictly improve the assets of both banks $v$ and $w$. Since the goal is to rescue $v$ in distress, we study creditor-positive trades, in which $v$ improves and $w$ remains indifferent. We show that an optimal creditor-positive trade that maximizes the assets of $v$ can be computed in polynomial time. It also yields a (weak) Pareto-improvement for all banks in the entire network. In networks with default cost, we obtain a trade in polynomial time that weakly Pareto-improves all assets over the ones resulting from the optimal creditor-positive trade. We generalize these results to trading multiple claims for which $v$ is the creditor. Instead, when trading claims with a common debtor $u$, we obtain NP-hardness results for computing trades in networks with default cost that maximize the assets of the creditors and Pareto-improve the assets in the network. Similar results apply when $w$ donates to multiple banks in networks with default costs. For networks without default cost, we give an efficient algorithm to compute optimal donations to multiple banks.

cs.GT↗