Multiperiod Security Markets with Differential Information :

We model multiperiod securities markets with differential information. A price system that admits no free lunches is related to martingales when agents have rational expectations. We introduce the concept of resolution time, and show that a better informed agent and a less informed agent must agree on the resolution times of commonly marketed events if they have rational expectations and if there are no free lunches. It then follows that if all elementary events are marketed for a less informed agent then any price system that admits no free lunches to a better informed agent must eliminate any private information asymmetry between the two. We provide an example of a dynamically fully revealing price system that is arbitrage free and yields elementarily complete markets. * Graduate School of Business, Stanford University, Stanford California 94305. †Alfred P. Sloan School of Management, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139. We acknowledge conversations with Michael Harrison and Andreu Mas–Colell, and the helpful comments of two referees. Tech-