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Efficient risk simulations for linear asset portfolios in the $$t$$-copula model. (English) Zbl 1176.91150
Summary: We consider the problem of calculating tail probabilities of the returns of linear asset portfolios. As a flexible and accurate model for the logarithmic returns we use the $$t$$-copula dependence structure and marginals following the generalized hyperbolic distribution. Exact calculation of the tail-loss probabilities is not possible and even simulation leads to challenging numerical problems. Applying a new numerical inversion method for the generation of the marginals and importance sampling with carefully selected mean shift we develop an efficient simulation algorithm. Numerical results for a variety of realistic portfolio examples show an impressive performance gain.

##### MSC:
 91G10 Portfolio theory
##### Software:
ghyp; LBFGS-B; R; Runuran
Full Text:
##### References:
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