Insider Trading with Penalties
Sylvain Carr\'e (EPFL), Pierre Collin-Dufresne (EPFL), Franck Gabriel

TL;DR
This paper analyzes a one-period Kyle model with insider trading penalties, establishing equilibrium existence and uniqueness, and characterizing optimal penalties that balance price efficiency and fairness, considering various regulatory constraints.
Contribution
It provides the first analytical characterization of equilibrium and optimal penalties in insider trading models with penalties, including extensions with budget constraints and different penalty types.
Findings
Equilibrium exists and is unique for a wide class of penalties.
Optimal penalties increase with small orders and flatten for large orders.
Penalties influence trade volume, price functions, and incorporate information about extreme events.
Abstract
We consider a one-period Kyle (1985) framework where the insider can be subject to a penalty if she trades. We establish existence and uniqueness of equilibrium for virtually any penalty function when noise is uniform. In equilibrium, the demand of the insider and the price functions are in general non-linear and remain analytically tractable because the expected price function is linear. We use this result to investigate the trade off between price efficiency and 'fairness': we consider a regulator that wants to minimise post-trade standard deviation for a given level of uninformed traders' losses. The minimisation is over the function space of penalties; for each possible penalty, our existence and uniqueness theorem allows to define unambiguously the post-trade standard deviation and the uninformed traders' losses that prevail in equilibrium.Optimal penalties are characterized in…
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