Traditional correlation-based approach under normality to dependence modeling is no longer adequate, as dependence of extreme events must be modeled and the scale-invariant measures of dependence might be considered. With this problem in popularity has come a rise in the need for modeling multivariate dependence with various types of dependence structure. In recent years there has been increasing applications of copulas in many fields. The copula-based approach is implemented by specifying the margins and the dependence structure represented by a certain type of copula function. Firstly, the stable distribution is considered contrary to the customarily adopted ones on marginal specifications. Secondly, two elliptical copulas and three most commonly used families of Archimedean copulas are employed in parameter estimation and model selection. This book reviews some related academic literatures, gives references for further reading for methodology, provides financial applications of copulas in risk management, offers a many-faceted comparison and discussions on dependence modeling, and suggests some directions for further research.

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