Star-Shaped Risk Measures

Abstract

One of the mantras of risk measurement is the avoidance of risk concentration. However, most formal approaches to the topic actually require more than this. In “Star-Shaped Risk Measures,” Castagnoli, Cattelan, Maccheroni, Tebaldi, and Wang study this property “in purity” for monetary risk measures. They show that it unites value at risk and convex risk measures, it is amenable to aggregation of opinions, and it leads to treatable optimization, thanks to a meaningful functional representation. They also show its ubiquitous presence in several fields of decision making under uncertainty.