Insider trading with penalties

We consider a Kyle (1985) one-period model where insider trading may be subject to a penalty that is increasing in trade size. We characterize the solution - the equilibrium price and optimal trading strategy explicitly and establish existence and uniqueness for an arbitrary penalty function for the case of uniformly distributed noise. We use this framework to capture the difference between legal and illegal insider trading, and identify the set of 'efficient penalty functions' that would be optimal for a regulator that seeks to minimize expected uninformed traders' losses for a given level of price informativeness. Simple policies consisting of a fixed penalty upon nonzero trades belong to this set and can be used to implement any efficient outcome. Using numerical analysis, we show the robustness of our results to different distributional assumptions. (c) 2022 Elsevier Inc. All rights reserved.