Correlated risks, bivariate utilityand optimal choices

In this paper, we consider a décision-maker facing a financial risk flanked by a backgroundrisk, possibly non-financial, such as health or environmental risk. A decision has to be madeabout the amount of an investment (in the financial dimension) resulting in a future benefiteither in the same dimension (savings) or in the order dimension (environmental quality orhealth improvement). In the first case, we show that the optimal amount of savings decreasesas the pair of risks increases in the bivariate increasing concave dominance rules of higherdegrees which express the common preferences of all the decision-makers whose twoargumentutility function possesses direct and cross derivatives fulfilling some specificrequirements. Roughly speaking, the optimal amount of savings decreases as the two risksbecome "less positively correlated" or marginally improve in univariate stochastic dominance.In the second case, a similar conclusion on optimal investment is reached under alternativeconditions on the derivatives of the utility function....