Mhmed Mesfioui (Université du Québec à Trois-Rivières)

Title: Comonotonicity and its applications in dependence modelling.

Abstract: The so-called trivariate reduction method is a popular approach widely used to construct multivariate distributions. It is well known that this method has two major drawbacks. On the one hand, it can only model positive dependence; on the other hand, it cannot always span the full range of positive correlation. To remedy these drawbacks, the comonotonicity notion can be used to construct new shock model which, contrary to the original, spans all possible degrees of dependence. The first part of this presentation will show how this novel idea can be used to construct a new family of bivariate exponential distributions having an interesting stochastic representation. This new distribution models the full range of positive correlations and improve the Marshall-Olkin bivariate exponential distribution. Some properties of the proposed model as well as an extension to negative dependence will be discussed. The second part of the talk emphasizes the usefulness of the comonotonicity to derive the best bounds for certain concordance measures in noncontinuous setting. Some applications in actuarial science will be presented.