This paper studies the dynamic asset allocation problem faced by an infinitivelylived commodity-based sovereign wealth fund under incomplete markets. Since the non-tradable stream of commodity revenues is finite, the optimal consumption and investment strategies are time dependent. Using data from the Norwegian Petroleum Fund, we find that the optimal demand for equity should decrease gradually from 60 to 40 percent over the next 60 years. However, the solution is particularly sensitive to the correlation between oil and stock price changes. We also estimate wealthequivalent welfare losses, relative to the optimal rule, when following alternative suboptimal investment rules.