Before revision: In this paper, the market extension of set-valued risk measures for models with proportional transaction costs is linked with set-valued risk minimization problems. 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.
After revision: New versions of the set-valued average value at risk (AV@R) is defined and its market extension and corresponding risk minimization problems are studied.