Abstracts

We discuss risk measures for financial positions in a multi-asset setting, representing the minimum amount of capital to raise and invest in admissible portfolios in order to meet a prescribed acceptability constraint. We investigate the interplay between the acceptance set and the set of admissible portfolios, with a special focus on continuity properties and dual representations. To avoid degenerate representations, we need to ensure the existence of specific extensions of the underlying pricing functional. We characterize when such extensions exist. Applications to conical market models, set-valued risk measures, optimal risk sharing, and superhedging with shortfall risk are provided.