Fractional Claims Trades and Donations in Financial Networks

2025-02-10

AI Summary

This paper investigates mechanisms for mitigating individual bank distress and curbing systemic risk contagion in financial networks via partial debt trading and unconditional liquidity donations. We propose a creditor-priority trading model and formally establish, for the first time, the Pareto-improving property of fractional debt trading and donations. Integrating game theory, graph theory, and optimization, we characterize computational complexity boundaries in multi-creditor/multi-recipient settings: under zero default costs, we design polynomial-time algorithms achieving optimal forward trading and multi-bank donations; under positive default costs, we construct weakly Pareto-improving solutions. We rigorously prove that both multi-creditor trading and multi-donor donation problems are NP-hard. Our results provide a computationally tractable theoretical framework and algorithmic guarantees for systemic risk mitigation.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Multiagent Systems: Mechanism Design
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

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.

Problem

• Improving financial networks via fractional claims trading
• Mitigating systemic risks through creditor-positive trades
• Optimizing donations and trades in networks with default costs

Innovation

• Fractional claims trading
• Polynomial-time optimization
• Creditor-positive trades