Fabio Maccheroni (Bocconi University) : Risk Measures: Rationality and Diversification

 When there is uncertainty about interest rates (typically
due to either illiquidity or defaultability of zero coupon bonds) the
cash-additivity assumption on risk measures becomes problematic. When this
assumption is weakened, to cash-subadditivity for example, the equivalence
between convexity and the diversification principle no longer holds. In
fact, this principle only implies (and it is implied by) quasiconvexity. For
this reason, in this paper quasiconvex risk measures are studied. We provide
a dual characterization of quasiconvex cash-subadditive risk measures and we
establish necessary and sufficient conditions for their law invariance. As a
byproduct, we obtain an alternative characterization of the actuarial mean
value premium principle.