Risk Aversion and Risk Premiums with Dependent Risks

By using a general bivariate utility function, this paper provides the conditions under which agents would like to remove primary risk in the presence of other dependent risk. For small risks, the conditions for retaining primary risk along with other dependent risk are also provided. The results of this paper indicate that the risk attitude to primary risk depends not only on the dependence relation between the risks, but also on the sign of the second-order cross derivatives of the utility function. In addition, agents also estimate the relative magnitude between the covariance of the risks and variance of the primary risk when they consider retaining the primary risk. Moreover, this paper examines the relation between risk premium for removing all risk simultaneously and those for removing risk sequentially. Rey’s (2003a) method to compare the total risk premium with the sum of the partial risk premiums is generalized to the case where there exists dependence relation between risks.