We consider the problem of an insurer who enters into a repeated relationship with a set of risk averse agents in the presence of ex post verification costs. The insurer wishes to minimize the expected cost of providing these agents a certain expected utility level. We characterize the optimal contract between the insurer and the insured agents. We then apply the analysis to the provision of deposit insurance. Our results suggest—in a deposit insurance context—that it may be optimal to utilize the discount window early on, and to make deposit insurance payments only later, or not at all.