In this paper, we consider a multivariate shortfall risk measure with scenario-dependent allocation weights and examine its properties such as convexity and quasi-convexity. For fixed allocation weights, we show that the resulting risk measure is a convex systemic risk measure in which case the...

Utility-based shortfall risk (SR) measure proposed by (F\”ollmer and Schied, 2002) has been well studied in risk management and finance. In this paper, we revisit the concept from insurance premium perspective. We show under some moderate conditions that the indifference equation-based...