Optimal Bailouts in Diversified Financial Networks
Krishna Dasaratha, Santosh Venkatesh, Rakesh Vohra
TL;DR
The paper tackles the problem of optimally selecting bailouts in diversified financial networks, where defaults generate costly spillovers and capital injections can trigger repayment cascades. It shows NP-hardness in general, but proves that when network structure follows a stochastic block model, the optimal bailout can be implemented via a simple index policy tied to firms' endowments and their block centrality, justified by a graphon continuum limit. By introducing a directed graphon formulation and analyzing extremal cutoff equilibria, the authors derive a spillover matrix $\mathbf{B}$ and an explicit, tractable method for allocating cash injections across blocks, with exact formulas for equalizing marginal benefits and the budget constraint $\frac{1}{2}\sum_k a_k y_k^2 = K$ in the linear-endowment case. They show that these continuum results translate to large finite networks and illustrate the insights with core–periphery and random SBM-inspired examples, offering a practical framework for regulatory interventions that mitigate contagion while minimizing total injections.
Abstract
Widespread default involves substantial deadweight costs which could be countered by injecting capital into failing firms. Injections have positive spillovers that can trigger a repayment cascade. But which firms should a regulator bailout so as to minimize the total injection of capital while ensuring solvency of all firms? While the problem is, in general, NP-hard, for a wide range of networks that arise from a stochastic block model, we show that the optimal bailout can be implemented by a simple policy that targets firms based on their characteristics and position in the network. Specific examples of the setting include core-periphery networks.