ABSTRACT: Using the concept of set-valued portfolios, it is possible to incorporate dependencies between the distribution of the multivariate gain and the exchange rules. The set-valued portfolio is considered acceptable if it possesses a selection (i.e. a random vector that alsmost surely belongs to it) with all individually acceptable components. The corresponding set-valued risk measure is said to be a selection risk measure. The talk surveys its main properties, discusses the primal and dual representation, gives examples, and shows how to approximate its values from below and from above using rather elementary arguments. Applications of selection risk measures to the practical risk assessment are also presented. A special attention is paid to applications of selection risk measures to risk assessment of financial groups.