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The group


The overall objective of the group is the study and analysis of random dynamical systems. Our interests lay in both
continuous-time models and discrete-time models (i.e., random walks) alike. A number of problems have
interested us along the years. Me mention specially non-Markovian dynamics, diffusions in disordered media and
escape and first-passage problems in random environments among others.

From the late nineties we have progressively turned our attention to a particular random environment: financial markets.
In the new field of econophysics, and by using our previous knowledge in stochastic physical systems, we have developed
several tools and models aimed to account for non-standard features and imperfections of markets which clearly deviate from
the so-called "perfect market hypothesis" which is the cornerstone of many economic theories.

Among our latest developments we may single out the application of the continuous random walk technique to deal with financial problems,
particularly for high-frequency data; a thorough study of stochastic volatility models which show and quantify many of the market deficiencies
(eg., fat tails, biass, clustering, etc...) and finally the application of first-passage techniques to risk control.