[영문]People have heterogenous life expectancies: women live longer than men, rich people live longer than poor people, and healthy people live longer than sick people. People are also subject to heterogenous out-of-pocket medical expense risk. We construct a rich structural model of saving behavior for retired single households that accounts for this heterogeneity, and we estimate the model using AHEAD data and the method of simulated moments. We find that the risk of living long and facing high medical expenses goes a long way toward explaining the elderly's savings decisions. Specifically, medical expenses that rise quickly with both age and permanent income can explain why the elderly singles, and especially the richest ones, run down their assets so slowly. We also find that social insurance has a big impact on the elderly's savings.