Consistent modeling of risk averse behavior with spectral risk measures: Wächter/Mazzoni revisited

Wächter and Mazzoni (2013) (W/M) have proposed a procedure to consistently link traditional expected utility (EU)-theory with modern spectral risk measures (SRMs). They construct a corresponding W/M-risk measure which induces the same preference ordering as the decision maker's initial utility function does. In this note, we revisit W/M's procedure and show that it violates the axiomatic foundation of the underlying decision rules: Within the general part of the procedure that builds on an auxiliary equivalent probability measure, the emerging W/M-risk measure does not satisfy the axiomatic properties of SRMs. The specific part of the procedure that singles out a preferred equivalent probability measure links two decision rules of which neither does the initial one respect the axioms of EU-theory, nor is the emerging one in line with the SRM-axioms.