Chaos in Economics and Finance

Now, on the other hand, we can remark that, concerning the use of deterministic chaotic systems, each community may have different strategies. They do not use the same models, nor the same information set. Most mathematicians work with analytical expressions and characterize their models under specific assumptions to decide if they can exhibit specific chaotic behaviors, characterized by specific properties, following varied definitions of 'chaos'. The economists generally use analytical systems corresponding to a specific modelling problem. These systems depend on few parameters and one purpose is to detect the range of these parameters in which they can lead to stable or unstable behaviors. Bifurcation theory is often a basis of their studies. Generally economists do not follow the roads of physicists. Indeed, physicists are interested by questions relative to universal laws, and in economics the trend is to understand and document differences. In finance, practitioners do not use analytical systems and want to use chaos theory to robustify their forecasts: most of the work is empirical. In statisitics, work concerns estimation theory and tries to prove robustness of estimates of the Lyapunov exponents or the embedding dimension, for instance. They are also interested in re-building orbits and forecasting on the attractors.