The present paper studies optimal monetary policy when the representative agent assumption is abandoned and financial wealth heterogeneity across households is introduced. Incomplete markets make households incapable of perfectly insuring against interest rate and inflation risk, creating a trade-off between price level and debt-servicing stabilization. We derive a welfare-based loss function for the policymaker, which includes an additional target related to the cross-sectional distribution of household debt. The extent of the deviation from price stability depends on the initial level of debt dispersion. Using U.S. microdata to calibrate the model, we find an optimal inflation volatility equal to almost 20 percent of the actual volatility of the last 15 years. Finally, the paper studies the design of optimal simple implementable rules. Superinertial rules, which imply a hump-shaped interest rate response to shocks, significantly outperform standard rules.