Learning from arbitrage

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.