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Abstract This paper studies a hierarchical risk model where an accident can cause a combination of different types of claims, whose sizes could be dependent. In addition, the frequencies of accidents that cause the different combinations of claims are dependent. We first derive formulas for computing risk measures, such as the Tail Conditional Expectation and Tail Variance of the aggregate losses for a portfolio of businesses. Then, we present formulas for performing the associated capital allocation to different types of claims in the portfolio. The main tool we used is the moment (or size-biased) transform of the multivariate distributions.
Gao et al. (Tue,) studied this question.