Before revision:  As a particular example, the set-valued average value at risk (AV@R) is defined and its market extension and corresponding risk minimization problems are studied. We show that for a finite probability space the calculation of the values of AV@R reduces to linear vector optimization problems which can be solved using known algorithms.
After revision:  As a particular example, the set-valued average value at risk for multivariate risks are introduced by generalizing the well-known certainty equivalent representation to the set-valued case. The first "regulator" version is independent from any market model whereas the second version, called the market extension, takes trading opportunities into account. Essential properties of both versions are proven and an algorithmic approach is provided which admits to compute the values of AV@R reduces to linear vector optimization problems which can be solved using known algorithms.