Stock Market Insider Trading in Continuous Time with Imperfect Dynamic Information ∗ Albina Danilova † Department of Mathematical Sciences Carnegie Mellon University October 16, 2018 This paper studies the equilibrium pricing of asset shares in the presence of dynamic private information. The market consists of a risk-neutral informed agent who observes the firm value, noise traders, and competitive market makers who set share prices using the total order flow as a noisy signal of the insider’s information. I provide a characterization of all optimal strategies, and prove existence of both Markovian and non Markovian equilibria by deriving closed form solutions for the optimal order process of the informed trader and the optimal pricing rule of the market maker. The consideration of non Markovian equilibrium is relevant since the market maker might decide to re-weight past information after receiving a new signal. Also, I show that a ) there is a unique Markovian equilibrium price process which allows the insider to trade undetected, and that b ) the presence of an insider increases the market informational efficiency, in particular for times close to dividend payment. Abstract arXiv:1607.00035v1 [q-fin.MF] 30 Jun 2016 $^{∗}$I benefited from helpful comments from Peter Bank, Rene Carmona, Christian Julliard, Dmitry Kramkov, Michael Monoyios, Andrew Ng, Bernt Øksendal and seminar and workshop participants at 4th Oxford - Princeton Workshop, 14th Mathematics and Economics Workshop – University of Oslo, Stochastic Filtering and Control Workshop – Warwick University and Warwick Business School. $^{†}$Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA 15213-3890, USA, e-mail: danilova@andrew.cmu.edu 1