University of Birmingham > Talks@bham > Optimisation and Numerical Analysis Seminars > LP-based identification of true and misspecified tail-dependence/Bernoulli matrices in large dimensions

## LP-based identification of true and misspecified tail-dependence/Bernoulli matrices in large dimensionsAdd to your list(s) Download to your calendar using vCal - Ralf Werner, University of Augsburg
- Thursday 17 November 2016, 12:00-13:00
- University House, room 108.
If you have a question about this talk, please contact Sergey Sergeev. In the context of market-, credit-, and operational risk, stochastic models allowing for tail dependence are considered indispensable in modern risk-management. Being difficult to estimate, it is often a matter of expert judgment to define a matrix 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 stochastic model can be constructed representing it. These problems, and the one-to-one connection to Bernoulli matrices, has been thoroughly studied on a theoretical level, but efficient numerical tests beyond d = 15 were so far deemed impossible. We add to the existing literature by exploiting the polyhedral geometry of the set of Bernoulli matrices. This allows to translate the above questions into a linear optimization problem with exponentially many variables. We demonstrate that the curse of dimensionality can be partially evaded by a specific column generation approach. For this purpose the additional structure in the constraints of the dual problem is exploited. Finally, we introduce a new stopping criterion for general column generation approaches by a suitable shrinkage of dual iterates to a dual Slater point. In essence, we can thus solve problems up to d = 40 in reasonable time. Joint work of Daniel Krause, Matthias Scherer, Jonas Schwinn, Ralf Werner This talk is part of the Optimisation and Numerical Analysis Seminars series. ## This talk is included in these lists:- Optimisation and Numerical Analysis Seminars
- School of Mathematics Events
- University House, room 108
Note that ex-directory lists are not shown. |
## Other listscomputer sience Type the title of a new list here Astrophysics Talks Series## Other talksWhen less is more - reduced physics simulations of the solar wind Hodge Theory: Connecting Algebra and Analysis Perfect matchings in random sparsifications of Dirac hypergraphs Sensing and metrology activities at NPL, India The development of an optically pumped magnetometer based MEG system Quantum simulations using ultra cold ytterbium |