Dependence structures of multiple risks play an essential role in many optimization problems in insurance,finance and risk management.In this talk,we propose a new class of dependence notions through arrangement increasing properties and develop different types of characterizations for these notions.The new notions incorporate many typical dependence structures that have been extensively studied in the literature,such as independence,comonotonicity,exchangeability,and dependence structures characterized by special copulas.We illustrate applications of these notions by several optimal portfolio selection problems.These applications extend existing studies to a more general context.