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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.