Some new results on information percolation

Abstract

We study the dynamics of a large number, N , of investors which have meetings by groups of m. We obtain an explicit formula for the solution of the associated non-linear system of differential equations. This formula is tractable and it enables us to show the asymptotic stability of a large class of models. One of those models can be thought of as an interacting portfolio market.

Existence and uniqueness of a steady state for an OTC market with several assets

“…It can be obtained, as in Ferland-Giroux [8], by a functional law of large numbers or by rewriting the system with a single probability kernel, the convex combination of the two kernels, and apply Theorem 1 of Bélanger-Giroux [1]. One could also appeal to the exact law of large numbers of Sun [13] and Duffie-Sun [7].…”

“…In Bélanger et al [1], another extension of the DGP model with several assets was considered and the existence and uniqueness of the steady state was established using the Intermediate Value Theorem. The authors also derived the value functions of the investors in order to obtain the prices at which investors trade with each other at that steady state and they showed moreover that the steady state is (exponentially) stable.This simpler extension of the DGP model can be called non-segmented market since it does not track the asset an investor wants, when she enters the market.…”