Abstract
We introduce the notion of cross-risk vulnerability which generalizes to the case of one risk in the presence of another non-insurable risk the concept of risk vulnerability introduced by Gollier and Pratt 1996 to deal with the univariate situation. We provide necessary and sufficient conditions for a bivariate utility function to exhibit cross-risk vulnerability both toward an actuarially neutral background risk and toward an unfair background risk. We also present several examples of families of bivariate utility functions which enjoy the desirable property of cross-risk vulnerability.
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