So far, research has only considered the case of a self-insurance independent premium when trying to model the interaction between self-insurance and market insurance. Ehrlich and Becker were in 1972 the first to formalize a model that accounted for marker insurance, self-insurance and self-protection. However they only found substitution between self-insurance and market insurance and this result has since been accepted as a general truth. Other authors have only focused on particular cases, such as unreliable self-insurance or increased risk aversion. This thesis shows that, accounting for the efforts invested in self-insurance, there may actually be cases with complementarity between self-insurance and market insurance. This is a significant result, as risk managers are theoretically supposed to maximize their utility, searching for the best trade-off between the risk control tools that are available to them. Associating self-insurance with market insurance may actually be a tool available to them that has been neglected in the past. Through this study, we are able to provide specific counter-examples to Ehrlich's and Becker's general results. This way, the reflection is brought upon the accuracy of risk management models and the possibility to account for self-insurance efforts in insurance contracts.