Many theoretical central bank models use short horizons and focus on a single tradeoff. However, in reality, central banks play complex, long-horizon games and face more than one tradeoff. We account for these strategic interactions in a simple infinite-horizon game with a novel tradeoff: tighter monetary policy deters financial imbalances, but looser monetary policy reduces the likelihood of insolvency. We term these factors discipline and stability effects, respectively. The central bank's welfare decreases with dependence between real and financial shocks, so it may reduce costs with correlation-indexed securities. An independent central bank cannot in general attain both low inflation and financial stability.