  In risk analysis, worst-case risk assessments are performed using maxitive
monetary risk measures. In this article, we investigate maxitive monetary risk
measures on subsets of \( L^0 \). We prove that a monetary risk measure is
maxitive and continuous from below if and only if it is a penalized worst-case
risk measure. We characterize the usual worst-case risk measure as the unique
maxitive and law-invariant monetary risk measure. We apply the results to large
deviation theory by providing a general criterion to establish a sharp large
deviation estimate of a sequence of probability measures. Additionally, we
prove new limit results for sequences of distorted expectations.
