Notions of multivariate dependence and their applications in optimal portfolio selections with dependent risks

•We propose the new dependence notions of LWSAI and WSAI.•We present properties of the new dependence notions of LWSAI and WSAI.•Dependent risks in portfolio section problems are modeled by the notions of dependence.•Many existing studies on optimal portfolio selections are extended to more general dependent risks.

In this paper, we propose the dependence notions of weakly stochastic arrangement increasing through left tail probability (LWSAI) and weakly stochastic arrangement increasing (WSAI) to model multivariate dependent risks. We derive properties and characterizations of these new notions and show that many existing dependence structures are the special cases of these notions of dependence. We apply the dependence notions of LWSAI and WSAI to the problem of optimal portfolio selections with dependent risks and generalize many existing studies.