Informed Opportunistic Trading and Price Optimal Control

Abstract

In this paper we address the issue of quantifying the incentive to invest or disinvest from an equity investment to benefit from discrepancies between its real value and its market value. Such a situation arises in particular when a manager trades her company's own stock. Two existing models for the impact of transactions on prices, one of them taking into account the total size of the market, are extended to the case of discrete transactions. They are derived from simple assumptions on the behaviour of market participants. 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.

JEL Classification: G31, G13