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DOI: 10.5445/IR/1000013434
DOI: 10.1007/s00186-007-0185-6
Zitationen: 13
Web of Science
Zitationen: 14

Dependence properties and comparison results for Lévy processes

Bäuerle, Nicole; Blatter, Anja; Müller, Alfred

In this paper we investigate dependence properties and comparison results for multidimensional Lévy processes. In particular we address the questions, whether or not dependence properties and orderings of the copulas of the distributions of a Lévy process can be characterized by corresponding properties of the Lévy copula, a concept which has been introduced recently in Cont and Tankov (2004) and Kallsen and Tankov (2006). It turns out that association, positive orthant dependence and positive supermodular dependence of Lévy processes can be characterized in terms of the Lévy measure as well as in terms of the Lévy copula. As far as comparisons of Lévy processes are concerned we consider the supermodular and the concordance order and characterize them by orders of the Lévy measures and by orders of the Lévy copulas, respectively. An example is given that the Lévy copula does not determine dependence concepts like multivariate total positivity of order 2 or conditionally increasing in sequence. Besides these general results we specialize our findings for subfamilies of Lévy processes. The last section contains some applications in fi ... mehr

Zugehörige Institution(en) am KIT Institut für Stochastik (STOCH)
Publikationstyp Zeitschriftenaufsatz
Jahr 2008
Sprache Englisch
Identifikator ISSN: 1432-2994
URN: urn:nbn:de:swb:90-134344
KITopen-ID: 1000013434
Erschienen in Mathematical Methods of Operations Research - ZOR
Band 67
Heft 1
Seiten 161-186
Schlagworte Lévy processes, dependence concepts, Lévy copula, dependence ordering, Archimedean copula, ruin times, option pricing
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