Particle Systems with Singular Interaction: Application in Systemic Risk Modeling

In this talk, I will analyze a system of particles with singular interaction through hitting times. Such systems have been used in Neuroscience, but are also well suited for modeling Systemic Risk. I will discuss the latter application and will proceed to the analysis of a large-population limit of the associated system. In particular, I will prove the Propagation of Chaos and will provide insights into the behavior of the limiting process. The main mathematical challenges of this work stem from the very singular type of interaction (i.e. threshold-type interaction) between the particles, which requires the use of non-standard mathematical methods. In particular, the limiting system is described by a non-local and non-linear PDE, whose well-posedness is established in our work. On the other hand, the aforementioned singularity of particles’ interaction is important from an application point of view, as it provides a natural mathematical description of important real-world phenomena, such as Systemic Crises in Finance and Synchronizations of Neurons in Neuroscience.

This is the joint work with Mykhaylo Shkolnikov.