Optimal Control of Interbank Contagion Under Complete Information
25 Pages Posted: 30 Aug 2013 Last revised: 3 Nov 2014
Date Written: December 28, 2013
We study a preferred equity infusion government program set to mitigate interbank contagion. Financial institutions are prone to insolvency risk channeled through the network of interbank debt and to the risk of bank runs. The government seeks to maximize, under budget constraints, the total net worth of the financial system or, equivalently, to minimize the dead-weight losses induced by bank runs. The government is assumed to have complete information on interbank debt. The problem of quantifying the optimal amount of infusions can be expressed as a convex combinatorial optimization problem, tractable when the set of banks eligible for intervention (core banks) is sufficiently, yet realistically, small.
We find that no bank has an incentive to withdraw from the program, when the preferred dividend rate paid to the government is equal to the government's outside rate of return on the intervention budget. On the other hand, it may be optimal for the government to make infusions in a strict subset of core banks.
Keywords: Systemic risk, Liquidity risk, Bank runs, Financial contagion, Financial Networks, Optimal Intervention, , Bail-outs
JEL Classification: C6, G18, G21, G28, G33
Suggested Citation: Suggested Citation