Random effects models are of particular importance in modeling heterogeneity. A commonly used random effects model for multivariate survival analysis is the frailty model. In this thesis, a special frailty model with an Archimedean dependence structure is used to model dependent risks. This modeling approach allows the construction of multivariate distributions through a copula with univariate marginal distributions as parameters. Copulas are constructed by modeling distribution functions and survival functions, respectively. Measures of the dependence are applied for the copula model selections. Tail-based risk measures for the functions of two dependent variables are investigated for particular interest. The statistical application of the copula modeling approach to an insurance data set is discussed where losses and loss adjustment expenses data are used. Insurance applications based on the fitted model are illustrated.
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