Classical and Quantum-Like Randomness and the Financial Market

The financial market is a complex dynamical system and, since the publication of the thesis of [1], there were performed numerous studies devoted to various aspects of random description of financial processes [2]. At the first stage of investigations Brownian motion was used to describe randomness of the financial market. This model provided a rather good approximation of some financial processes. However, later it became evident that the diversity of financial stochastic processes could not be reduced to Brownian motion. The next step was consideration of functionals of Brownian motion, especially, geometric Brownian motion [2]. Later there were considered other types of stochastic processes [2], in particular, general Levy processes.