A risk analysis for a system stabilized by a central agent

TL;DR

This paper models how systemic risk in a multi-agent system is affected by interactions with a central stabilizing agent, showing that stronger local-central interactions reduce systemic risk, while stronger central-to-mean field interactions increase it.

Contribution

It introduces a multi-agent model with a bistable central agent influencing local agents, analyzing how different interaction strengths impact systemic risk in the mean field limit.

Findings

Increasing local-central interaction reduces systemic risk.

Increasing central-to-mean field interaction increases systemic risk.

Systemic risk decreases with stronger local-central coupling.

Abstract

We formulate and analyze a multi-agent model for the evolution of individual and systemic risk in which the local agents interact with each other through a central agent who, in turn, is influenced by the mean field of the local agents. The central agent is stabilized by a bistable potential, the only stabilizing force in the system. The local agents derive their stability only from the central agent. In the mean field limit of a large number of local agents we show that the systemic risk decreases when the strength of the interaction of the local agents with the central agent increases. This means that the probability of transition from one of the two stable quasi-equilibria to the other one decreases. We also show that the systemic risk increases when the strength of the interaction of the central agent with the mean field of the local agents increases. Following the financial interpretation of such models and their behavior given in our previous paper (Garnier, Papanicolaou and Yang, SIAM J. Fin. Math. 4, 2013, 151-184), we may interpret the results of this paper in the following way. From the point of view of systemic risk, and while keeping the perceived risk of the local agents approximately constant, it is better to strengthen the interaction of the local agents with the central agent than the other way around.