Endogenous noise trackers in a Radner equilibrium

TL;DR

This paper proves the existence of an incomplete Radner equilibrium with endogenous noise trackers, analyzing how these affect welfare and market dynamics in a model with exponential investors.

Contribution

It introduces a model with endogenous noise trackers in Radner equilibrium and establishes existence through a coupled ODE system reduction.

Findings

Endogenous noise trackers can increase aggregate welfare under certain conditions.

Welfare effects depend non-trivially on model parameters and stock supply.

The model provides insights into the role of endogenous noise in financial markets.

Abstract

We prove the existence of an incomplete Radner equilibrium in a model with exponential investors and an endogenous noise tracker. We analyze a coupled system of ODEs and reduce it to a system of two coupled ODEs in order to establish equilibrium existence. As an application, we study the impact of the endogenous noise tracker on welfare by comparing to a model with an exogenous noise trader. We show that the aggregate welfare in the endogenous noise tracker model is bigger for a sufficiently large stock supply, but the welfare comparison depends in a non-trivial manner on the other model parameters.