Stock market insider trading in continuous time with imperfect dynamic information

Abstract

In this paper, I study 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 the 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 (1) there is a unique Markovian equilibrium price process that allows the insider to trade undetected and (2) the presence of an insider increases the market's informational efficiency, in particular, for times close to dividend payment.

Keywords:

• insider trading
• dynamic private information
• rational expectations equilibrium
• non-Markovian pricing rule
• linear filtering

AMS Subject Classification::

• 91B44
• 91B28
• 91A26
• 91B24
• 62M20

Acknowledgements

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.

Notes

^1. This is without loss of generality, since the extension to multiple information release times is straightforward.

^2. Setting will make conditions 2–4 exactly the same as in [2].