Distortion risk measure (DRM) plays a crucial role in risk measuring and managing, especially in insurance pricing. Various DRMs have been introduced but little is discussed about which DRM at hand should be chosen to address a decision maker (DM)'s risk attitude. This paper aims to fill out the...

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...

This paper reviews the various measures which have been used in the recent literature to assess how well donors allocate their aid across countries. We begin by proposing three desirable criteria for a measure of allocative performance, which make limited assumptions. We then show that all...