Stochastic process with multiplicative structure for the dynamic behavior of the financial market

A stochastic model with multiplicative noise has been proposed as a mathematical model for the prices dynamics of the financial market. We have presented a model which allows us to test within the same framework the comparative explanatory power of rational agents versus irrational agents with respect to facts of the financial market. We calculate the long range memory of the model and studied the behavior of the long tail distribution of the cumulative distribution of probabilities for the model with additive and multiplicative noise.