Comontonic Measures Of Multivariate Risks

Because of uncertainty and complexity, we need some certain assumptions to measure risks clearly and conveniently. The independence of each risk is in common use. But in fact they are not independent. There are complex dependencies between risk factors. Comonotonicity is an extreme dependence structure.In this paper, a new class of multivariate risk measures based on well-known char-acterization by S.Kusuoka of regular and coherent risk measures as maximal correlated functions is proposed. Firstly, this paper introduces characterization of Strongly Coher-ent Risk Measures to replace the current law invariance. subadditivity, and comonotonic-ity axioms equivalently. Secondly, the paper proposes a multivariate generalization of Kusuoka's theorem by an extension of the notion of comonotonicity to random vectors through generalized quantile functions called μ-comonotonicity. Finally, we show explicit examples of computation of the maximal correlation risk measure as Gaussian distribution with Specific parameters.