Design of an Experiment to Test Nonclassical Probabilistic Behavior of the Financial market

The recent crash demonstrated (once again) that the description of the financial market by present financial mathematics cannot be considered as totally satisfactory. We remind that nowadays financial mathematics is heavily based on the use of random variables and stochastic processes which are described by Kolmogorov’s measuretheoretic model for probability (“classical probabilistic model”). I speculate that the present financial crises is a sign (a kind of experiment to test validity of classical probability theory at the financial market) that the use of this model in finances should be either totally rejected or at least completed. One of the best candidates for a new probabilistic financial model is quantum probability or its generalizations, so to say quantum-like (QL) models. Speculations that the financial market may be nonclassical have been present in scientific literature for many years. The aim of this note is to move from the domain of speculation to rigorous statistical arguments in favor of probabilistic nonclassicality of the financial market. I design a corresponding statistical test which is based on violation of the formula of total probability (FTP). The latter is the basic in classical probability and its violation would be a strong sign in favor of QL behavior at the market.