Risk measures with comonotonic subadditivity or convexity on product spaces

In this paper, by an axiomatic approach, we propose the concepts of comonotonic subadditivity and comonotonic convex risk measures for portfolios, which are extensions of the ones introduced by Song and Yan(2006)Representation results for these new introduced risk measures for portfolios are given in terms of Choquet integralsLinks of these newly introduced risk measures to multi-period comonotonic risk measures are representedFinally, applications of the newly introduced comonotonic coherent risk measures to capital allocations are provided.