2022/11/28 by Jérôme Detemple, Detemple, Jerome, Scott Robertson +1
Decision Sciences · Economics, Econometrics and Finance · #91B69 #91G30 #Economic theories and models #FOS: Economics and business #Game Theory and Applications #Mathematical Finance (q-fin.MF)
paper · pdf · doi:10.48550/arxiv.2211.15573
openalex publication_date 2022/11/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 Ψ(XT), while the uninformed agent (``U'') has no private signal. Ψ 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,∞) 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.