Multiperiod security markets with differential information: Martingales and resolution times |
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| Affiliation: | 1. Université libre de Bruxelles, Department of Mathematics, Boulevard du Triomphe, CP 210, Brussels 1050, Belgium;2. Dipartimento di Matematica, Università degli Studi di Padova, Italy;3. De Vinci Research Center, Finance Group, Leonard de Vinci Pôle Universitaire, Paris La Défense, France;1. Department of Economics, Indiana University, Bloomington, IN 47405, USA;2. European University in St. Petersburg, 3 Gagarinskaya Street, St. Petersburg, 191187, Russia;3. St. Petersburg Institute for Economics and Mathematics (Russian Academy of Sciences), 36-38 Serpukhovskaya Street, St. Petersburg, 190013, Russia;4. St. Petersburg State University, 7/9 Universitetskaya nab., St. Petersburg, 199034, Russia;5. Department of Economics, Finance & Real Estate, Feliciano School of Business, Montclair State University, Montclair, NJ 07043, USA;1. Department of Mathematics, South China University of Technology, China.;2. Department of Mathematics and Risk Management Institute, National University of Singapore, Singapore.;3. Key Laboratory of Random Complex Structures and Data Science, Institute of Applied Mathematics, AMSS, Chinese Academy of Sciences, China. |
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| Abstract: | ![]()
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. |
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