Diversification and Risk Aversion with Two Risks

In this paper, we propose a definition of risk aversion and risk loving to one risk in the presence of another for an arbitrarily chosen size of exposure to the former risk. Restricting the set of bivariate utility functions that are risk averse to the former risk in isolation and correlation averse (correlation loving), risk loving or risk aversion with two risks according to our definition prevails, depending on whether the size of risk exposure is smaller or larger than a unique critical level, respectively, if, and only if, the two risks are negatively (positively) expectation dependent. We offer two applications regarding primary prevention for health risks and the motive for precautionary saving in the presence of wealth and interest rate risks to illustrate the usefulness of our concept of risk aversion and risk loving with two risks when the dependence structure of the underlying random variables is governed by the notion of expectation dependence