As demonstrated by Ehrlich and Becker [1972], Expected Utility Theory predicts that market insurance and self-insurance are substitutes, whilst surprisingly, market insurance and self-protection could be complements. This article examines the robustness of this conclusion, as well as its extensions under the Dual Theory of Choice [Yaari, 1987]. In particular, the non-reliability of self-insurance activities, background risk and asymmetric information are considered.