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Title: Aggregation of comonotone risks using robust distribution functions Authors:  Ignacio Montes - University of Oviedo (Spain) [presenting]
Abstract: Comonotonicity is a dependence structure modelling random variables that increase or decrease simultaneously. Comonotone random variables possess not only interesting mathematical properties, but they also appear in several applications, mainly in decision theory and finance. In the latter field, understanding random variables as risks, there are three well-known properties related to comonotonicity: (i) there exists a known expression for the cdf of the aggregated risks under comonotonicity; (ii) the aggregation of the risks assuming comonotonicity is a conservative approximation of the aggregated risk with respect to the stop-loss premium; and (iii) the VaR of the aggregation of comonotone risks can be decomposed as the aggregation of the VaR of the marginal risks. A natural question appears: what happens when the probability distribution of the risks is only partially known? In those cases, the cdfs can be replaced by robust cdfs (known as $p$-boxes in the imprecise probability literature) giving lower and upper bounds to the values of the real but unknown cdfs. The three aforementioned properties of comonotone risks are shown still hold when using robust cdfs, and proves that one robust model performing particularly well in this setting is the Kolmogorov model.