In this paper, we analyze under which conditions a self-supporting insurance guaranty fund can be beneficial for the policyholders in an incomplete market. Within the analyzed setting, we find out that in general, if existent, the potential advantages from its introduction cannot be fairly divided among the participating insurers. Thereby, we have to expect systematic wealth transfers between the policyholders of different insurance companies. We introduce a framework for utility-based fund charges as a solution to this problem.