Insider Trading with Penalties

Abstract

We establish existence and uniqueness of equilibrium in a generalized one-period Kyle (1985) model where insider trading can be subject to a penalty cost that is non-decreasing in the trade size.
The result is obtained for uniform noise and holds for general penalty functions. Uniqueness is among all non-decreasing strategies.
We construct the equilibrium price and optimal insider trading policy explicitly and find that, except for quadratic penalties, both are non-linear functions of, respectively, the trading volume and the liquidation value. We characterize the set of optimal penalties a regulator would choose to maximize price informativeness for given level of expected uninformed traders' losses. Efficient penalties eliminate small rather than large trades. We extend the analysis to the case where implementable regulations are constrained by a budget constraint and consider the robustness of our findings to different distributional assumptions.

Keywords: Kyle model, non-linear equilibria, existence and uniqueness, market microstructure, insider trading, market regulation, efficient penalties

JEL Classification: C72, G14