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.

Some new results on Dufffie-type OTC markets

“…It is the tool that enables us, for instance, to state proposition 5. Its proof follows the lines of the proof of the main result in Bélanger-Giroux [1].…”

“…We add exponential times to obtain a marked Poisson process whose marks are horizontal lines linking the agents participating in a given interaction. This enabled us, in Bélanger-Giroux [1], to describe the limit law of an agent, under an appropriate conditioning, as a countable convex combination on trees which is, as we have shown in section 3 of that article, the global solution of the associated differential equation on the space of probability laws.…”

“…We have shown Bélanger-Giroux [1] that the Cauchy problem has a unique solution which can be expressed, by conditioning on the number of interactions up to time t, and then by the component's history. Such conditionings give us…”

“…We recall that A n denotes the set of m-ary ordered trees with n internal nodes. Then A n constitutes a set of random trees if we assume that every m-ary tree in A n is equally likely, namely of probability 1 #m(n) . The tree starting at P s vertical line at time t with intensity 1 and which at time 0 has intensity (m − 1)n + 1 and that same number of leaves.…”

“…In section 3 of Bélanger-Giroux [1], the explicit formulas for the Wild sums were used to obtain the convergence of the solution of the evolution equation to a steady state. This is one of the important applications permitted by the tractability of our explicit formulas.…”