Optimal Equity Infusions in Interbank Networks
35 Pages Posted: 13 Aug 2012 Last revised: 13 Feb 2013
Date Written: August 13, 2012
We study optimal equity infusions into a financial system represented as a hierarchical network with two classes of banks, prone to both the risk of insolvencies and the risk of runs by short term creditors. The government seeks to minimize, under budget constraints, the magnitude of the total loss in the system. Under complete information on interbank exposures, the problem can be expressed as a combinatorial optimization problem, tractable when the set of core banks is small. Under partial information on exposures, revealed over time, distress propagation under intervention is shown to become a Markov Decision Process. We reduce the dimensionality of the problem so as to make it numerically tractable. We find the optimal intervention policy as a result of Hamilton-Jacobi-Bellman equations. Our results show that, in presence of a relatively small fraction of banks that use short-term funding, the optimal strategy swiftly changes from a strategy to avoid insolvency to a strategy to avoid runs by short term creditors.
Keywords: systemic risk, liquidity risk, financial contagion, Markov decision process, optimal interventions
JEL Classification: C6, G01, G28
Suggested Citation: Suggested Citation