Optimal dissimulation control of insider trading under mandatory disclosure and quadratic penalty

Within the continuous-time Kyle framework, this paper develops an equilibrium model of insider trading under dual regulatory constraints: Mandatory public disclosure and quadratic economic penalties. By applying the Pontryagin maximum principle, we derive explicit closed-form solutions for all market equilibrium parameters. Three core findings are obtained. First, regulatory penalties curb insiders' aggressive terminal trading, reducing trading intensity and profits while preventing full private information incorporation into prices, leading to non-zero terminal residual information. Second, penalty constraints endogenously distort insiders' dissimulation strategies. Without penalties, full dissimulation $ \sigma_x = \sigma_z $ (where $ \sigma_x $ denotes the insider's dissimulation noise volatility and $ \sigma_z $ denotes the market noise volatility) is optimal; with penalties, the optimal dissimulation volatility decreases with the growth of penalty intensity, and insiders abandon dissimulation entirely $ (\sigma_x = 0) $ as the penalty tends to infinity. Third, there exists a unique critical dissimulation ratio $ k^*\approx0.6823 $ for terminal residual information. When the dissimulation ratio is below this critical threshold, terminal residual information in the no-disclosure regime is larger than that under mandatory disclosure, and the opposite holds when the ratio exceeds the threshold. Moreover, insiders' equilibrium profit without mandatory disclosure is always higher than that under disclosure for any admissible dissimulation ratio. We also briefly examine the optimal penalty design within this framework. These results revise the oversimplified assumption widely adopted by existing analogous models that fixes dissimulation volatility equal to market noise volatility, and provide theoretical guidance for the design of insider trading regulatory policies.