The empirical established non-Gaussian behavior of asset price fluctuations is studied using an analytical approach. The analysis is based on a nonlinear Fokker-Planck equation with a self-organized feedback-coupling term, devised as a fundamental model for price dynamics. The evidence, and the analytical form of the memory term, are discussed in the context of statistical physics. It will be suggested that the memory term in leading order offers a power law dependence with an exponent $\theta .$ The stationary solution of the probability density leads asymptotically to a truncated Lévy distribution, the characteristic exponent $\beta$ of which is related to the exponent $\theta$ by $\beta =3/\theta -1.$ The empirical data can be reproduced by $\theta \simeq 5/4.$

• Received 26 September 2000

DOI:https://doi.org/10.1103/PhysRevE.64.026104