On multivariate countermonotonic copulas and their actuarial application

Bangwon Ko, Jae Youn Ahn

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


Extreme positive dependence, also known as comonotonicity or the Fréchet upper bound, has been an important concept in insurance since it describes the most dangerous financial behaviors. However, there is no generally agreed upon definition for extreme negative dependence because the corresponding Fréchet lower bound does not exist. To resolve this, a set of copulas under the name of d-Countermonotonicity (d-CTM) has been proposed to define extreme negative dependence rather than a single copula. The set of d-CTM copulas can be quite useful in various optimization problems. In this paper, we investigate various properties of d-CTM with more emphasis on the practical issues of actual optimization problems. As an application to insurance, we explore the effect of risk pooling under extreme dependence by adopting the so-called measure of uncertainty.

Original languageEnglish
Pages (from-to)387-396
Number of pages10
JournalLobachevskii Journal of Mathematics
Issue number4
StatePublished - 1 Jul 2016

Bibliographical note

Publisher Copyright:
© 2016, Pleiades Publishing, Ltd.


  • Countermonotonicity
  • Minimal Copula
  • Variance Minimization


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