Modeling stock market dynamics based on conservation principles

In this paper, a deterministic framework for modeling stock market dynamics is presented. The model is based on assets conservation principles and consists of a series of di0erential equations describing the dynamics of assets trading, and a (nonlinear) functional equation describing trade conservation (i.e., what is bought (sold) by one trader is sold (bought) by other traders). In this way, the dynamics of the assets and its price are determined by the trading dynamics. An equilibrium price is achieved when certain demand=supply equations are satis2ed. Attention is devoted to a speci2c case, in which the trading activity is based on trader groups and an in2nitely divisible asset. Numerical simulations show that even a single stock market asset with two classes of investors can display oscillatory price dynamics and instability. Moreover, the underlying oscillatory time-series display a discontinuous erratic-type behavior. c © 2001 Published by Elsevier Science B.V.