This contribution to the proceedings of the Cracow meeting on `Applicationsof Random Matrix Theory' summarizes a series of studies, some old and othersmore recent on financial applications of Random Matrix Theory (RMT). We firstreview some early results in that field, with particular emphasis on theapplications of correlation cleaning to portfolio optimisation, and discuss theextension of the Marcenko-Pastur (MP) distribution to a non trivial `true'underlying correlation matrix. We then present new results concerning differentproblems that arise in a financial context: (a) the generalisation of the MPresult to the case of an empirical correlation matrix (ECM) constructed usingexponential moving averages, for which we give a new elegant derivation (b) thespecific dynamics of the `market' eigenvalue and its associated eigenvector,which defines an interesting Ornstein-Uhlenbeck process on the unit sphere and(c) the problem of the dependence of ECM's on the observation frequency of thereturns and its interpretation in terms of lagged cross-influences.
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