Systemic Risks

Modeling systemic risks

The term ‘systemic risk’ denotes the risk that a whole system consisting of many interacting agents fails. We see systemic risk as a macroscopic property that emerges from the nonlinear interactions of agents.

This differs from a conventional view that focuses on the probability of single extreme events, e.g. earthquakes or big meteors hitting the earth, that seriously damage the system. It also differs from a perspective, for example, used in finance, where a single agent is big enough to damage the whole system - which leads to the notion of systemic importance.

In addition to all these ingredients, our systemic perspective emphasizes the impact of individual failure exerted on other agents. I.e., the systemic failure can start with the failure of a few agents which is amplified both by interaction mechanisms and by systemic feedback. This can lead to failure cascades which span a significant part of the system.

We provide a general framework for modelling systemic risk which was first applied to fully connected networks and is being extended to networks with arbitrary degree distribution from a formal theoretical point of view. Since we also allow for nodes to have heterogeneous robustness, various applications and extensions of the existing models are possible. They include credit networks, supply networks or social online networks where cascades of leaving users may threaten the existence of the platform.

Our approach is based on the concept of complex networks, where agents are represented by nodes in a network, whereas their interactions are modelled by links between them. Both nodes and links can follow their own dynamics and influence each other by feedback effects. In order to understand the emergence of systemic risk, we have to model (a) the internal dynamics of the agents, which is largely neglected in other approaches, (b) the interaction dynamics of the agents (in particular the network topology), (c) macroscopic or systemic feedback, i.e. the impact of changing external conditions, (d) trend reinforcement, i.e. the fact that interactions are path dependent and depend on the history of previous interactions.