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Extreme values of a portfolio of Gaussian processes and a trend

Hüsler, Jürg ; Schmid, Christoph

In: Extremes, 2005, vol. 8, no. 3, p. 171-189

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    Titre
    • Extreme values of a portfolio of Gaussian processes and a trend
    Auteur
    • Hüsler, Jürg. Institut für mathematische Statistik und Versicherungslehre, Universität Bern, Sidlerstrasse 5, 3012, Bern, Switzerland
    • Schmid, Christoph. Institut für mathematische Statistik und Versicherungslehre, Universität Bern, Sidlerstrasse 5, 3012, Bern, Switzerland
    Type de document
    • Postprint
    Identifiant OAI-PMH
    • oai:doc.rero.ch:319006
    Summary
    We consider the extreme values of a portfolio of independent continuous Gaussian processes $$\sum_{i=1}^{k}w_{i}X_{i}(t)$$ ( $$w_{i} \in \mathbb{R}, \; k \in \mathbb{N}$$ ) which are asymptotically locally stationary, with expectations $$E[X_{i}(t)]=0$$ and variances $$Var[X_{i}(t)]=d_{i}t^{2H_{i}}$$ $$(d_{i} \in \mathbb{R^{+}}, 00$$ with $$\beta > H_{i}$$ . We derive the probability $$P\{ \sup_{t>0} \sum_{i=1}^{k}w_{i}X_{i}(t) -ct^{\beta} > u \}$$ for $$u \rightarrow \infty$$ , which may be interpreted as ruin probability