Speaker: Yuyu Chen
Title: Robust risk aggregation techniques and applications
Abstract: Robust risk aggregation refers to the sum of individual risks with known marginal distributions and unspecified dependence structure, and it has been studied extensively with applications in banking and insurance. We study the robust risk aggregation of two risks under the constraint that one risk is smaller than or equal to the other. The largest aggregate risk in concave order is attained by the directional lower coupling. The result is further generalized to calculate the bounds of tail risk measures. Our numerical results suggest that the new bounds on risk measures with the extra order constraint can greatly improve those with full dependence uncertainty.
The set of distributions of the robust risk aggregation is called the aggregation set. We next investigate ordering relations between two aggregation sets for which the sets of marginals are related by two simple operations: distribution mixtures and quantile mixtures. Intuitively, these operations ``homogenize" marginal distributions by making them similar. As a general conclusion from our results, more ``homogeneous" marginals lead to a larger aggregation set. Finally, we provide applications on portfolio diversification under dependence uncertainty.
