Dependence properties and comparison results for L¨¦vy processes

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• 作者：Nicole B?uerle ; Anja Blatter and Alfred M¨¹ller
• 关键词：L¨¦vy processes ; Dependence concepts ; L¨¦vy copula ; Dependence ordering ; Archimedean copula ; Ruin times ; Option pricing
• 刊名：Mathematical Methods of Operations Research (ZOR)
• 出版年：2008
• 出版时间：February, 2008
• 年：2008
• 卷：67
• 期：1
• 页码：161-186
• 全文大小：276.5 KB

文摘

In this paper we investigate dependence properties and comparison results for multidimensional L¨¦vy processes. In particular we address the questions, whether or not dependence properties and orderings of the copulas of the distributions of a L¨¦vy process can be characterized by corresponding properties of the L¨¦vy copula, a concept which has been introduced recently in Cont and Tankov (Financial modelling with jump processes. Chapman & Hall/CRC, Boca Raton, 2004) and Kallsen and Tankov (J Multivariate Anal 97:1551–1572, 2006). It turns out that association, positive orthant dependence and positive supermodular dependence of L¨¦vy processes can be characterized in terms of the L¨¦vy measure as well as in terms of the L¨¦vy copula. As far as comparisons of L¨¦vy processes are concerned we consider the supermodular and the concordance order and characterize them by orders of the L¨¦vy measures and by orders of the L¨¦vy copulas, respectively. An example is given that the L¨¦vy 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 L¨¦vy processes. The last section contains some applications in finance and insurance like comparison statements for ruin times, ruin probabilities and option prices which extends the current literature.