Bidimensional Risk Aversion: The Cardinal Sin

Attitudes towards bidimensional risk depend both on the shape of the indifference map under certainty (an ordinal property) and on the degree of concavity of the utility function representing preferences under risk (a cardinal property). A decomposition of the risk premium in a cardinal and an ordinal component is built on the new notion of “compensated risk aver- sion”. The balance between the two components is shown to depend on the direction of the risk. These results are also linked to stochastic orders accounting for risks along general directions. Keywords: Multivariate Risk Aversion, Correlation Aversion, Risk Premium, Submodularity, Compensated Risk Aversion.