Forecasts are always wrong. Still, they paint potential future scenarios and provide a platform for policy decisions today. This is what gives forecast such a high salience in political debates about the effects of population aging. The paper aims at gauging the effect of population aging on hospital expenses in Germany. We use a probabilistic forecast model comprising a stochastic demographic component that exploits historical mortality trends, a stochastic cost component based on typical hospital costs over the life-course, and a quality measure of medical progress, which builds on past advances in hospital treatment. Three different scenarios are constructing, yielding 3 important results. Firstly, there is an increase in overall hospital expenditure until the German baby boomers will die out (2040 to 2050). Secondly, the increase is comparably moderate because the average individual costs are likely to decline as elderly health improves and since medical progress has an ambiguous influence on hospital expenditures. Finally, the cost increase varies significantly by gender and disease.