We study indefinitely-lived assets in experimental markets and find that the traded prices of these assets are on average about 40% of the risk neutral fundamental value. Neither uncertainty about the value of total dividend payments nor horizon uncertainty about the duration of trade can account for this low traded price, while the temporal resolution of payoff uncertainty plays a crucial role. We show that an Epstein and Zin (1989) recursive preference specification together with probability weighting can rationalize the low traded prices observed in our indefinite-horizon asset markets, while risk attitudes do not play such an important role.