An extended family of financial-risk measures

Abstract

Recalling the class of risk measures introduced by Stone [1973], the authors survey measures from different academic disciplines - including psychology, operations research, management science, economics, and finance - that have been introduced since 1973. We introduce a general class of risk measures that extends Stone's class to include these new measures. Finally, we give four axioms that describe necessary attributes of a good financial risk measure and show which of the measures surveyed satisfy these. We demonstrate that all measures that satisfy our axioms, as well as those that do not but are commonly used in finance, belong to our new generalized class.