In this paper we focus on the incentive to invest or disinvest in equity shares to benefit from discrepancies between their real value and their market prices, based on privileged information. Such a situation arises in particular when a manager trades his company's own stock. An existing simple model for the impact of transactions on prices is extended to the case of discrete transactions. This model is used to represent the impact of the informed agent's transactions. A probabilistic approach is proposed to determine the optimal control applied to the market price by the informed agent. Analytical solutions are derived to calculate the value of "realigning the price" for an informed market participant, and the properties of the controlled market price are discussed.