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.