Dynamic Equilibrium with Insider Information and General Uninformed Agent Utility

TL;DR

This paper analyzes a continuous-time economy with asymmetric information, allowing for general utility functions for uninformed agents, and introduces a new method to establish the existence of partial communication equilibria.

Contribution

It extends equilibrium analysis to agents with general utility functions and develops a novel approach for proving equilibrium existence under asymmetric information.

Findings

Existence of partial communication equilibrium with general preferences.

Equilibrium prices characterized in small and large risk aversion limits.

Recovery of the uninformed agent's signal from equilibrium prices in single-asset case.

Abstract

We study a continuous time economy where agents have asymmetric information. The informed agent (``$I$''), at time zero, receives a private signal about the risky assets' terminal payoff $\Psi(X_T)$, while the uninformed agent (``$U$'') has no private signal. $\Psi$ is an arbitrary payoff function, and $X$ follows a time-homogeneous diffusion. Crucially, we allow $U$ to have von Neumann-Morgenstern preferences with a general utility function on $(0,\infty)$ satisfying the standard conditions. This extends previous constructions of equilibria with asymmetric information used when all agents have exponential utilities and enables us to study the impact of $U$'s initial share endowment on equilibrium. To allow for $U$ to have general preferences, we introduce a new method to prove existence of a partial communication equilibrium (PCE), where at time $0$, $U$ receives a less-informative signal than $I$. In the single asset case, this signal is recoverable by viewing the equilibrium price process over an arbitrarily short period of time, and hence the PCE is a dynamic noisy rational expectations equilibrium. Lastly, when $U$ has power (constant relative risk aversion) utility, we identify the equilibrium price in the small and large risk aversion limits.