Multiperiod security markets with differential information. (English) Zbl 0608.90006

Summary: 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.


91B24 Microeconomic theory (price theory and economic markets)
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[1] Chung, K.L.; Williams, R., An introduction to stochastic integration, (1983), Birkhäuser Boston, MA · Zbl 0527.60058
[2] Dellacherie, C.; Meyer, P., Probabilities and potential, (1978), North-Holland Amsterdam, New York
[3] Dellacherie, C.; Meyer, P., Probabilities and potential B: theory of martingales, (1982), North-Holland New York
[4] Duffie, D., Stochastic equilibria: existence, spanning number, and the ‘no expected financial gain from trade’ hypothesis, Econometrica, 54, 1161-1184, (1986) · Zbl 0602.90025
[5] Duffie, D.; Huang, C., Implementing Arrow-Debreu equilibria by continuous trading of few long lived securities, Econometrica, 53, 1337-1356, (1985) · Zbl 0576.90014
[6] Harrison, J.M.; Kreps, D., Martingales and arbitrage in multiperiod securities markets, Journal of economic theory, 20, 381-408, (1979) · Zbl 0431.90019
[7] Huang, C., Information structure and equilibrium asset prices, Journal of economic theory, 31, 33-71, (1985) · Zbl 0553.90027
[8] Huang, C., Information structures and viable price systems, (), forthcoming. · Zbl 0606.90012
[9] Huang, C.; Kreps, D., Intertemporal preferences with a continuous time dimension: an exploratory study, (1985), MIT Cambridge, MA, Mimeo.
[10] Jacod, J., Calcul stochastique et problémes de martingales, (), no. 714 · Zbl 0414.60053
[11] Jeulin, T.; Yor, M., Grossissement d’une filtration et semimartingale. formules explicites, (), no. 649 · Zbl 0411.60045
[12] Kreps, D., A note on ‘fulfilled expectations’ equilibria, Journal of economic theory, 14, 32-43, (1977) · Zbl 0351.90011
[13] Kreps, D., Arbitrage and equilibrium in economies with infinitely many commodities, Journal of mathematical economics, 8, 15-35, (1981) · Zbl 0454.90010
[14] Liptser, R.; Shiryayev, A., Statistics of random processes I: general theory, (1977), Springer New York · Zbl 0364.60004
[15] Memin, J., Espaces de semi martingales et changement de probabilité, Zeitschrift für wahrscheinlichkeitstheorie, 52, 9-39, (1980) · Zbl 0407.60046
[16] Schaeffer, H., Topological vector spaces, (1971), Springer New York
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