Risk measures under model uncertainty: A Bayesian viewpoint

We introduce two kinds of risk measures with respect to some reference probability measure, which both allow for a certain order structure and domination property. Analyzing their relation each other leads the question when minimax inequality is actually an equality. then provide conditions under corresponding robust measures, being defined as supremum over all induced by set can be represented classically in terms one single measure. focus particular on mixture measure obtained via mixing using prior, represents instance regulator's beliefs. The classical representation interpreted Bayesian approach measures.