Optimal Network Compression

TL;DR

This paper formulates the problem of optimally compressing financial networks to reduce systemic risk, proves its computational complexity, and analyzes the effects of compression on network fragility under shocks.

Contribution

It introduces a general formulation for optimal network compression in financial systems, proves NP-hardness, and studies the impact on systemic risk and network robustness.

Findings

Optimal network compression can reduce systemic risk.

NP-hardness of the optimal compression problem.

Network topology influences robustness and fragility.

Abstract

This paper introduces a formulation of the optimal network compression problem for financial systems. This general formulation is presented for different levels of network compression or rerouting allowed from the initial interbank network. We prove that this problem is, generically, NP-hard. We focus on objective functions generated by systemic risk measures under shocks to the financial network. We use this framework to study the (sub)optimality of the maximally compressed network. We conclude by studying the optimal compression problem for specific networks; this permits us to study, e.g., the so-called robust fragility of certain network topologies more generally as well as the potential benefits and costs of network compression. In particular, under systematic shocks and heterogeneous financial networks the robust fragility results of Acemoglu et al. (2015) no longer hold generally.