A dynamical model of non regulated markets

The main focus of this work is to understand the dynamics of non regulated markets. The present model can describe the dynamics of any market where the pricing is based on supply and demand. It will be applied here, as an example, for the German stock market presented by the Deutscher Aktienindex (DAX), which is a measure for the market status. The duality of the present model consists of the superposition of the two components the long and the short term behaviour of the market. The long term behaviour is characterised by a stable development which is following a trend for time periods of years or even decades. This long term growth (or decline) is based on on the development of fundamental market figures. The short term behaviour is described as a dynamical evaluation (trading) of the market by the participants. The trading process is described as an exchange between supply and demand. In the framework of this model there the trading is modelled by a system of nonlinear differential equations. The model also allows to explain the chaotic behaviour of the market as well as periods of growth or crashes. PCAS numbers: 01.75.+m, 05.40.+j, 02.50.Le Contribution to the technical seminar 22/12/98, DESY-IfH Zeuthen