Fractional Model of Market Behavior: a New Modeling Approach

Stochastic models are a standard tool for analyzing the behavior of markets in response to changes that happen in the environments, in which these markets function. This paper presents a novel model of market analysis that uses the fractional calculus as its main tool. The model is based on the assumption that the market value is proportional to the energy-informational content of the value bearing item. The model is developed starting from fundamental principles, such as energy conservation which is valid for all cases. The evolution of the market value is described by means of the Volterra integral equation that describes the major and minor trends in the value variation. Using the data available for public access on the Internet at http://www.gold.org, the model developed in this study has been validated by showing that the evolution of the gold price can be quite adequately modeled by considering single major disturbance acting upon the world market.