Short Communication: A Note on Robust Risk-Sharing with Convex Risk Measures

We study the general properties of robust inf-convolution and risk-sharing for convex risk measures under uncertainty in random variables. Our approach has uncertainty on a set of multivariate random variables dependent on the allocation decision. In our main result and contribution, we characterize the acceptance set, penalty term, and necessary and sufficient conditions for optimality. Moreover, we provide concrete examples for uncertainty sets, especially based on closed balls under p-norms and Wasserstein distance. We also expose examples that relate our approach to the alternative where uncertainty is treated in a univariate setting.