Understanding and mitigating systemic risk is an important ongoing challenge in financial networks. We study an approach to rescue a bank in distress based on the idea of claims trading , a notion defined in Chapter 11 of the U.S. Bankruptcy Code. We formalize the idea in the context of the seminal model of financial networks by Eisenberg and Noe [9]. Given two banks v and w , we consider the operation that w takes over some claims of v and in return gives liquidity to v (or creditors of v ) to ultimately rescue v (or mitigate contagion effects). We study structural properties and computational complexity of decision and optimization problems arising from this trading operation. When trading claims for which v is the creditor, we show that there is no trade in which both banks v and w strictly improve their assets. While deciding the existence of a trade, in which v profits strictly and w remains indifferent, can be NP -hard, we provide FPTAS’es to approximate such a trade, even when banks settle their debt using general monotone payment functions. When trading claims with a common debtor, we show positive and negative results that crucially depend on the payment functions.