Some new results on Dufffie-type OTC markets

TL;DR

This paper generalizes Wild sums from statistical physics to model complex OTC markets, providing explicit solutions for systems with multiple interacting components and kernels.

Contribution

It introduces explicit formulas for the evolution of large systems with multiple interacting kernels, extending Wild sums to OTC market models.

Findings

Explicit solutions for systems with m components

Generalization of Wild sums to OTC market dynamics

Applicability to models with multiple kernels

Abstract

The extended Wild sums considered in this article generalize the classi- cal Wild sums of statistical physics. We first show how to obtain explicit solutions for the evolution equation of a large system where the interactions are given by a single, but general, interacting kernel which involves m components, for a fixed m >= 2. We then show how to retain the explicit formulas for the case of OTC market models where the dynamics is more directly described by two (or more) kernels.