A Framework for Measures of Risk under Uncertainty

A risk analyst assesses potential financial losses based on multiple sources of information. Often, the assessment does not only depend specification loss random variable, but also various economic scenarios. Motivated by this observation, we design a unified axiomatic framework for evaluation principles which quantifies jointly variable and set plausible probabilities. We call such an principle generalized measure. present series relevant theoretical results. The worst-case, coherent, robust measures are characterized via different sets intuitive axioms. establish equivalence between few natural forms law invariance in our framework, technical subtlety therein reveals sharp contrast traditional one. Moreover, coherence strong derived from combination other conditions, provides additional support coherent as Expected Shortfall over Value-at-Risk, issue management practice.