Payment stablecoins are privately issued digital money with the potential to enhance payment efficiency, foster innovation, and improve financial inclusion. At the same time, they are vulnerable to runs and associated welfare losses. One way to lower run risk is to require stablecoin issuers to hold safe assets. But doing so may lower issuers’ profitability and thus their incentive to provide stablecoins, hampering payment innovation and product variety. This paper offers a theoretical framework to navigate the tradeoff between maintaining stability and incentivizing issuance. Based on the Diamond and Dybvig (1983) model of bank runs, the paper shows that an unregulated private equilibrium is suboptimal. Stablecoin issuers hold risky assets to maximize profits, increasing run risk. A social planner can improve the equilibrium by requiring the backing of stablecoins with a safe asset (such as central bank reserves in a narrow bank setting), and creating conditions for other sources of revenue for issuers (such as central bank reserves remuneration or policies for payment data utilization). The model offers a baseline for the ongoing policy discussion while identifying considerations for further study.