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TZID:Europe/Paris
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BEGIN:VEVENT
UID:1-222@lptms.universite-paris-saclay.fr
DTSTART:20140109T143000Z
DTEND:20140109T163000Z
DTSTAMP:20131219T074901Z
URL:http://www.lptms.universite-paris-saclay.fr/seminars/tri-semianaire-de
 -physique-marc-potters/
SUMMARY:Tri-sémianaire de Physique Statistique : Marc Potters - LPTMS\, sa
 lle 201\, 2ème étage\, Bât 100\, Campus d'Orsay - 9 Jan 14 14:30
DESCRIPTION:A Random Matrix Bayesian framework for out-of-sample quadratic 
 optimization\nMarc Potters\, Capital Fund Management (CFM)\, Paris\nLarge 
 empirical sample covariance matrices exhibit a distribution of eigenvalues
  well described by the work of Marcenko and Pastur. As a consequence\, mea
 n-variance optimization using the sample-covariance matrix gives disastrou
 s out-of-sample results as the methods overweighs modes of spuriously low 
 variance.  We propose here a Bayesian framework for the true covariance m
 atrix whose conditional expectation should be used for mean-variance optim
 ization. While the framework is quite general\, we explore a few rotationa
 lly invariant priors\, namely shifted-Wigner\, Wishart and inverse-Wishart
 . While the latter is easily solved and leads to linear shrinkage the othe
 r two give rise to interesting matrix integrals. A naïve matrix saddle po
 int gives an approximate solution\, the zeroth order term in a systematic 
 expansion in planar Feynman diagrams.  The first few terms of this expans
 ion can be computed. The eigenvalue saddle point involves the orthogonal v
 ersion of the Itzykson-Zuber integral that we solve exactly only in a very
  special case. We also discuss a numerical method that allows the computat
 ion of the conditional mean by Monte Carlo simulation. The methodology pre
 sented here has direct applications in finance (portfolio optimization) an
 d should be applicable to other fields of “big data.”
LOCATION:LPTMS\, salle 201\, 2ème étage\, Bât 100\, Campus d'Orsay\, 15 
 Rue Georges Clemenceau\, Orsay\, 91405\, France
GEO:48.698185;2.181768
X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=15 Rue Georges Clemenceau\,
  Orsay\, 91405\, France;X-APPLE-RADIUS=100;X-TITLE=LPTMS\, salle 201\, 2è
 me étage\, Bât 100\, Campus d'Orsay:geo:48.698185,2.181768
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