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Rank-based methods for modeling dependence between loss triangles. (English) Zbl 1394.91205
Summary: In order to determine the risk capital for their aggregate portfolio, property and casualty insurance companies must fit a multivariate model to the loss triangle data relating to each of their lines of business. As an inadequate choice of dependence structure may have an undesirable effect on reserve estimation, a two-stage inference strategy is proposed in this paper to assist with model selection and validation. Generalized linear models are first fitted to the margins. Standardized residuals from these models are then linked through a copula selected and validated using rank-based methods. The approach is illustrated with data from six lines of business of a large Canadian insurance company for which two hierarchical dependence models are considered, i.e., a fully nested Archimedean copula structure and a copula-based risk aggregation model.

MSC:
91B30 Risk theory, insurance (MSC2010)
62H05 Characterization and structure theory for multivariate probability distributions; copulas
62P05 Applications of statistics to actuarial sciences and financial mathematics
Software:
nacopula; TwoCop; NSM3; QRM
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