Risk Measures

The present review of (financial) risk measures, prepared for the Encyclopaedia of Actuarial Science, first distinguishes two conceptions of risk. Risk of the first kind conceives risk as the magnitude of (one- or two-sided) deviations from a target, whereas risk of the second kind conceives risk as necessary capital or necessary premium, respectively. Some important axiomatic characterizations of risk measures are reviewed, including a characterization of a correspondence between risk measures of the first kind and risk measures of the second kind. Finally, a detailed overview of different risk measures of the first and second kind is presented.