Fractional Claims Trades and Donations in Financial Networks

TL;DR

This work extends the Eisenberg–Noe financial network model by introducing fractional claims trades and donations as tools to mitigate contagion from distressed banks. It develops a default hierarchy and a polynomial-time LP-based framework to compute creditor-positive trades that maximize a distressed creditor’s assets, with weak Pareto-improvements across the network, and extends these results to multiple incoming and outgoing edges. It also proves NP-hardness for certain multi-edge trades in networks with default costs, while showing efficient algorithms for donations and for fractional trades without default costs. The paper connects fractional trades to debt swaps and reveals rich algorithmic structure, including exact solvability in several cases and compelling open problems around unbounded returns and joint optimization. These results provide principled computational methods for targeted rescue strategies and deepen understanding of network resilience under strategic asset transfers.

Abstract

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.

Figures (1)

• Figure 1: Left: Network $\mathcal{F}$ from our introductory example. Boxed node labels indicate external assets. Edge labels indicate payments. All edges have a liability of 4. Middle: Network $\mathcal{F}'$ after binary trade with $\beta = 1$ and $\rho = a_w^x = 3$. Right: Network $\mathcal{F}'$ after fractional trade with $\beta = 3/4$ and $\rho = a_w^x = 3$.

Theorems & Definitions (16)

• Proposition 1
• Proposition 2
• Definition 3
• Definition 4
• Proposition 5
• Theorem 6
• Corollary 7
• Theorem 8
• Corollary 9
• Lemma 10