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Journal Articles Journal of Mathematical Economics Year : 1999

On risk aversion with two risks


We consider necessary and sufficient conditions for risk aversion to one risk in the presence of another non-insurable risk. The conditions (on the bivariate utility function) vary according to the conditions imposed on the joint distribution of the risks. If only independent risks are considered, then any utility function which is concave in its first argument will satisfy the condition of risk aversion. If risk aversion is required for all possible pairs of risks, then the bivariate utility function has to be additively separable. An interesting intermediate case is obtained for random pairs that possess a weak form of positive dependence. In that case, the utility function will exhibit both risk aversion (concavity) in its first argument, and bivariate risk aversion (submodularity).

Dates and versions

hal-00540256 , version 1 (26-11-2010)



Marco Scarsini, Israel Finkelshtain, Offer Kella. On risk aversion with two risks. Journal of Mathematical Economics, 1999, Vol. 31, N°2, pp. 239-250. ⟨10.1016/S0304-4068(97)00058-X⟩. ⟨hal-00540256⟩


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