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CATEGORIES:Optimisation and Numerical Analysis Seminars
SUMMARY:LP-based identification of true and misspecified t
ail-dependence/Bernoulli matrices in large dimensi
ons - Ralf Werner\, University of Augsburg
DTSTART:20161117T120000Z
DTEND:20161117T130000Z
UID:TALK2241AT
URL:/talk/index/2241
DESCRIPTION:In the context of market-\, credit-\, and operatio
nal risk\, stochastic models allowing for tail dep
endence are considered indispensable in modern ris
k-management. Being difficult to estimate\, it is
often a matter of expert judgment to define a matr
ix of pairwise tail-dependence coefficients. Given
a d x d matrix\, however\, it is rather difficult
to decide if (i) this matrix is indeed a possible
tail-dependence matrix\, and (ii) how a stochasti
c model can be constructed representing it.\nThese
problems\, and the one-to-one connection to Berno
ulli matrices\, has been thoroughly studied on a t
heoretical level\, but efficient numerical tests b
eyond d = 15 were so far deemed impossible. We add
to the existing literature by exploiting the poly
hedral geometry of the set of Bernoulli matrices.
This allows to translate the above questions into
a linear optimization problem with exponentially m
any variables. We demonstrate that the curse of di
mensionality can be partially evaded by a specific
column generation approach. For this purpose the
additional structure in the constraints of the dua
l problem is exploited. Finally\, we introduce a n
ew stopping criterion for general column generatio
n approaches by a suitable shrinkage of dual itera
tes to a dual Slater point. In essence\, we can th
us solve problems up to d = 40 in reasonable time.
\n\nJoint work of Daniel Krause\, Matthias Scherer
\, Jonas Schwinn\, Ralf Werner\n
LOCATION:University House\, room 108
CONTACT:Sergey Sergeev
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