The concept of genuine savings has in recent years become widely accepted as a dynamic welfare indicator, which first appeared in Weitzman (1976) and then "formalized" by Pearce and Atkinson (1993). This paper attempts to generalize this concept in a stochastic setting using the Dasgupta-Heal-Solow growth model under the Merton (1975) type of population growth uncertainty. It is shown that the formula for genuine savings under uncertainty also involves a variance component reflecting the welfare loss from risk aversion (cf. Li and Lofgren, 2012). Moreover, the welfare implications of the risk-adjusted genuine savings on depletable resource management are explored.