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The ability to make optimal decisions under uncertainty remains importantacross a variety of disciplines from portfolio management to power engineering.This generally implies applying some safety margins on uncertain parametersthat may only be observable through a finite set of historical samples.Nevertheless, the optimized decisions must be resilient to all probableoutcomes, while ideally providing some measure of severity of any potentialviolations in the less probable outcomes.It is known that the conditionalvalue-at-risk (CVaR) can be used to quantify risk in an optimization task,though may also impose overly conservative margins. Therefore, this paperdevelops a means of co-controlling the value-at-risk (VaR) level associatedwith the CVaR to guarantee resilience in probable cases while providing ameasure of the average violation in less probable cases. To further combatuncertainty, the CVaR and VaR co-control is extended in a distributionallyrobust manner using the Wasserstein metric to establish an ambiguity setconstructed from finite samples, which is guaranteed to contain the truedistribution with a certain confidence.

Co-Control of VaR and CVaR forData-Driven Stochastic Demand Response Auction