Insider trading with penalties in continuous time

This paper addresses the question of how insiders internalize the additional penalties to trade in a continuous time Kyle model. The penalties can be interpreted as non-adverse selection transaction costs or legal penalties due to illegal insider trading. The equilibrium is established for general asset distribution. In equilibrium, the insider does not disseminate her private information fully into the market prices. Moreover, she always trades a constant multiple of the discrepancy between her own valuation and her forecast of market price right before her private information becomes public. In the particular case of normally distributed asset value, the trades are split evenly over time for sufficiently large penalties, with trade size proportional to the return on the private signal. Although the noise traders lose less when penalties increase, the insider’s total penalty in equilibrium is non-monotone since the insider trades little when the penalties surpasses the value of the private signal. As a result, a budget-constrained regulator runs an investigation only if the benefits of the investigation are sufficiently high. Moreover, the optimal penalty policy is reduced to choosing from one of two extremal penalty levels that correspond to high and low liquidity regimes. The optimal choice is determined by the amount of noise trading and the relative importance of price informativeness.