How Damage Diversification Can Reduce Systemic Risk

TL;DR

This paper introduces damage diversification (DD) as a novel risk mitigation strategy in complex networks, demonstrating its potential to reduce systemic risk compared to traditional exposure diversification (ED) by focusing on distributing losses rather than exposures.

Contribution

The study develops a generalized branching process model for weighted networks and analytically compares DD and ED, highlighting DD's effectiveness in lowering systemic risk and identifying key nodes.

Findings

Damage diversification reduces systemic risk more effectively than exposure diversification.

Analytical expressions for average cascade size and node failure probabilities are derived.

The model identifies systemically relevant nodes even with varying weight distributions.

Abstract

We consider the problem of risk diversification in complex networks. Nodes represent e.g. financial actors, whereas weighted links represent e.g. financial obligations (credits/debts). Each node has a risk to fail because of losses resulting from defaulting neighbors, which may lead to large failure cascades. Classical risk diversification strategies usually neglect network effects and therefore suggest that risk can be reduced if possible losses (i.e., exposures) are split among many neighbors (exposure diversification, ED). But from a complex networks perspective diversification implies higher connectivity of the system as a whole which can also lead to increasing failure risk of a node. To cope with this, we propose a different strategy (damage diversification, DD), i.e. the diversification of losses that are imposed on neighboring nodes as opposed to losses incurred by the node itself. Here, we quantify the potential of DD to reduce systemic risk in comparison to ED. For this, we develop a branching process approximation that we generalize to weighted networks with (almost) arbitrary degree and weight distributions. This allows us to identify systemically relevant nodes in a network even if their directed weights differ strongly. On the macro level, we provide an analytical expression for the average cascade size, to quantify systemic risk. Furthermore, on the meso level we calculate failure probabilities of nodes conditional on their system relevance.