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Learning from arbitrage

Author

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  • Lionel De Boisdeffre

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, CATT - Centre d'Analyse Théorique et de Traitement des données économiques - UPPA - Université de Pau et des Pays de l'Adour)

Abstract

We extend the refinement of information process introduced by Cornet and De Boisdeffre (Econ Theory 38:287–293, 2009) to a model with uncountably many states of nature. This setting has the larger scope. It encompasses, in particular, the Cornet and De Boisdeffre (J Math Econ 38:393–410, 2002) model, where agents may have private information, and De Boisdeffre (Book in Honor of the 65th anniversary of Prof. Bernard Cornet, 2015) model, where they may have private information, anticipations and beliefs. With no price expectation a la Radner (Econometrica 40:289–303, 1972, Econometrica 47:655–678, 1979), and even no price to observe, we show how agents can always infer information from markets, whenever required, and narrow down their anticipation sets, until all arbitrage is precluded. When this result is applied to our latter model (2015), the path to equilibrium discards rational expectations. That is, equilibrium prices and anticipations may jointly be reached by agents, who are unaware of how equilibrium prices are determined, and simply observe, respond and learn from arbitrage opportunities on available portfolios, as they would do on actual financial markets.

Suggested Citation

  • Lionel De Boisdeffre, 2016. "Learning from arbitrage," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-01871266, HAL.
  • Handle: RePEc:hal:cesptp:hal-01871266
    DOI: 10.1007/s40505-015-0082-8
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    Cited by:

    1. de Boisdeffre, Lionel, 2022. "Dropping rational expectations," Mathematical Social Sciences, Elsevier, vol. 115(C), pages 37-46.
    2. de Boisdeffre, Lionel, 2021. "Equilibrium in incomplete markets with differential information: A basic model of generic existence," Mathematical Social Sciences, Elsevier, vol. 110(C), pages 53-62.

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