Model space of economic events

Abstract

A method for constructing the model or virtual space of economic events when economic objects can be considered as material ones is suggested. We describe change of share rates in time at stock markets as the potential difference of attracted bodies in time in this virtual space. Each share of each enterprise is displayed by a single particle with a unit “charge”. It is shown that the random value of potential difference at the origin of coordinates measured at a definite time interval has the probability density coinciding with the known distribution of “Levy flights” or “Levy walks”. A distribution of alteration in time of the “Standard and Poor” index value obtained by Mantegna and Stanley (they shown that it is the “Levy walks” distribution too) (Mantegna and Stanley, Nature 376 (1995) 46) is used for determination of the introduced potential dependence on coordinates in the model space. A simple phenomenological model of interaction potential is introduced. The potential law of each particle turns out to be closed to r −2.14 in the minimum possible three-dimensional model space. This model permits calculation of time of random potential correlations at a certain point of the model space. These correlations could characterize the time period of making a decision by an investor at stock exchange. It is shown that this time is notably shorter in unstable periods (1987). A “microscopical” model of interaction in the virtual space is also discussed.