We investigate the dual role of money as a self-insurance device and a means of payment when perfect risk sharing is not possible, and when the two roles of money are disentangled. We use a variant of Lagos-Wright (2005) where agents face a risk in the centralized market (CM): in the decentralized market (DM) money's main role is as a means of payment, while in the CM it is as a self-insurance device. We show that state-contingent inflation rates can improve agents' ability to self-insure in the CM, thereby improving the terms of trade in the DM. We then characterize the optimal monetary policy.JEL codes: C78, E40, E52