Analysis and Review of Risk Measures: VAR, CVAR, What to Use?

The actuarial–financial literature does not reach a consensus on which risk measures should be used in practice. Our paper studies the properties of risk measures that can help avoid some inconsistencies observed with popular measures, like VaR or Conditional Value at Risk (CVaR). Two new families of risk measures are defined; complete and adapted risk measures. In particular, we study distortion risk measures and characterize them as complete/adapted, in terms of the linearity of the distortion function, rather than its non–differentiability, as suggested by Wang (2002, AFIR Coll.).