Nº 19-68: Insider Trading with Penalties

We establish existence and uniqueness of equilibrium in a generalised one-period Kyle (1985) model where insider trades can be subject to a size-dependent penalty. The result is obtained by considering uniform noise and holds for virtually any penalty function. Uniqueness is among all non-decreasing strategies. The insider demand and the price functions are in general non-linear, yet tractable.
We apply this result to regulation issues. We show analytically that the penalty functions maximising price informativeness for given noise traders' losses eliminate small rather than large trades. We generalise this result to cases where a budget constraint distorts the set of penalties available to the regulator.