"We study the general properties of robust convex risk measures as worst-case values under uncertainty on random variables. We establish general concrete results regarding convex conjugates and sub-differentials. We refine some results for closed forms of worstcase law invariant convex risk measures under two concrete cases of uncertainty sets for random variables: based on the first two moments and Wasserstein balls."
The concept proposes verifiable uncertainty akin to classical lotteries, suggesting it as a fundamental way to comprehend uncertainty. Rules are outlined for contrasting general events with verifiable lottery-like situations. Decision-making involves evaluating verifiable uncertainty differently from unverifiable uncertainty, allowing distinct attitudes and conservative handling of the latter. This approach forms a more solid theoretical basis for decision-making.
In 1921, Keynes and Knight stressed the distinction between uncertainty and risk. While risk involves calculable probabilities, uncertainty lacks a scientific basis for probabilities. Knightian uncertainty exists when outcomes can't be assigned probabilities. This poses challenges in decision-making and regulation, especially in scenarios like AI, urging caution for eliminating worst-case scenarios due to potential high costs and missed benefits.