One of the central problems which we are interested in is financial stylized facts. This is a common notion for a few observed properties of financial data that contrast with the standard equilibrium market theory based on such fundamentals as the efficient market hypothesis, blind price setting (tatonnement), investor rationality, utility optimization, etc. Among such facts there are, for example, the power-law tails of probability distribution functions of financial fluctuations, long memory of some observables like volatility, the negative cross-correlation between present price changes and their future amplitude (the leverage effect), and the multifractal structure of various financial fluctuations. One may also count among the stylized facts the deviations from investor rationality causing herding behaviour that can lead to formation of market bubbles.
These empirical properties are especially interesting from a physicist's point of view since they are frequently observed in diverse out-of-equilibrium physical systems, including those that that are close to phase transitions. This analogy is a motivation for physics to apply its formalisms that have been developed in contexts of non-equilibrium statistical mechanics and theory of critical phenomena in an attempt to explain hitherto unexplained phenomena observed in financial markets.
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