Diversification for general copula dependence

Abstract

We generalize the extreme value analysis for Archimedean copulas (see ALINK, LÖWE and WÜTHRICH, 2003) to the non-Archimedean case: Assume we have d ≥ 2 exchangeable and continuously distributed risks X 1 , . . ., X d . Under appropriate assumptions there is a constant q d such that, for all large u, we have PThe constant q d describes the asymptotic dependence structure. Typically, q d will depend on more aspects of this dependence structure than the well-known tail dependence coefficient.

Asymptotic Tail Probabilities for Large Claims Reinsurance of a Portfolio of Dependent Risks

“…A similar problem is discussed by Albrecher et al (2006), Barbe et al (2006), Alink et al (2007) and Kortschak and Albrecher (2007), when a more general dependence structure is assumed. Since the ECOMOR and LCR reinsurances are linear combinations of the order statistics, studying the asymptotic tail probability for the losses associated with these reinsurance treaties is closely related to the aforementioned problem.…”

“…Note that we use the fact that h(x) = xh(1/x) holds. By using the same reasoning as Alink et al (2007), one can establish …”

Correlation order, merging and diversification

“…Asymptotic results concerning the diversification effect arising by aggregating dependent risks are considered in Alink et al (2005Alink et al ( , 2007, amongst others.…”

Computational methods for sums of random variables

“…Remark 3. 9. The use of gamma distribution and Laguerre polynomials links our approach to a well established technique called the Laguerre method.…”

“…The asymptotics in (5.7) also hold in many regimes where dependence has been introduced, cf. [75,167,8,9].…”