Generalized Lotka-Volterra (GLV) models extending the (70 year old) logistic equation to stochastic systems consisting of a multitude of competing auto-catalytic components lead to power distribution laws of the (100 year old) Pareto-Zipf type. In particular, when applied to economic systems,...

The 1990‰fs has been punctuated by a series of severe financial and currency crises: the Exchange Rate Mechanism (ERM) attacks of 1992; the Mexican peso collapse of 1994; the East Asian crisis of 1997; the Russian collapse of 1998; and the Brazilian devaluation of 1999. One striking characteristic of these...

The LLS stock market model (for a review see the book in Academic Press 2000: "Microscopic Simulation of Financial Markets; From Investor Behavior to Market Phenomena" by Levy, Levy and Solomon, ISBN: 0124458904) is a model of heterogeneous quasi-rational investors operating in a complex...

The paper develops a theoretical model of endogenous wealth distribution, showing that a logarithmic mean constraint in the maximum entropy formalism leads to a power law distribution. On the level of economic theory, the model implies two trade-offs: first, the higher the aggregate growth of...

In continuous time, diffusion processes have been used for modelling financial dynamics for a long time. For example the Ornstein-Uhlenbeck process (the simplest mean-reverting process)has been used to model non-speculative price processes. The Cox-Ingersoll-Ross process is widely used to model...