Aggregation of Dependent Risks with Heavy-Tail Distributions

Abstract

Straightforward methods to evaluate risks arising from several sources are specially difficult when risk components are dependent and, even more if that dependence is strong in the tails. We give an explicit analytical expression for the probability distribution of the sum of non-negative losses that are tail-dependent. Our model allows dependence in the extremes of the marginal beta distributions. The proposed model is flexible in the choice of the parameters in the marginal distribution. The estimation using the method of moments is possible and the calculation of risk measures is easily done with a Monte Carlo approach. An illustration on data for insurance losses is presented.

Risk aggregation considering probabilistic and consequential interactions: A general formulation with computational cost handling

“…How to accurately aggregate interacted risks has become increasingly popular in RM. Risk aggregation approaches, such as the copula method, the integrated multi‐criteria evaluation methodology, and the Choquet integral multiple linear regression model, are proposed (Bernard et al., 2014; Guillen et al., 2019; Li et al., 2010). These methods mainly rely on mature fuzzy theory or probabilistic mechanisms.…”