On risk aversion with two risks

We consider necessary and sufficient conditions for risk aversion to one ri sk in the presence of another non-insurable risk. The conditions (on the bi variate utility function) vary according to the conditions imposed on the j oint distribution of the risks. If only independent risks are considered, t hen any utility function which is concave in its first argument will satisf y the condition of risk aversion. If risk aversion is required for all poss ible pairs of risks, then the bivariate utility function has to be additive ly 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). (C) 1999 Elsevier Science S. A. All rights reserved.