Learning from arbitrage

We extend the refinement of information process presented in [3] to a model with uncountably many states of nature. This setting has the larger scope. It encompasses, in particular, the model of [3], where agents may have private information, and the model of [5], where they have private information, anticipations and beliefs. With no price model a la Radner (1972, 1979), and even no price to be observed, we show how agents may always infer information from ?nancial markets, whenever required, and narrow down their anticipation sets, until all arbitrage is precluded.