Dynamic equilibrium with insider information and general uninformed agent utility

Jerome Detemple and Scott Robertson

Mathematical Finance, 2025, vol. 35, issue 1, 111-160

Abstract: We study a continuous time economy where agents have asymmetric information. The informed agent (“I$I$”), at time zero, receives a private signal about the risky assets' terminal payoff Ψ(XT)$\Psi (X_T)$, while the uninformed agent (“U$U$”) has no private signal. Ψ$\Psi$ is an arbitrary payoff function, and X$X$ follows a time‐homogeneous diffusion. Crucially, we allow U$U$ to have von Neumann–Morgenstern preferences with a general utility function on (0,∞)$(0,\infty)$ 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$U$ to have general preferences, we introduce a new method to prove existence of a partial communication equilibrium (PCE), where at time 0, U$U$ receives a less‐informative signal than I$I$. 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$U$ has power (constant relative risk aversion) utility, we identify the equilibrium price in the small and large risk aversion limits.

Date: 2025
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https://doi.org/10.1111/mafi.12444

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Working Paper: Dynamic Equilibrium with Insider Information and General Uninformed Agent Utility (2024)
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