This paper examines the controversial problem of the choice of the social discount rate in development projects, by focusing on the investment required to adapt to climate change, considering the threats to food security and the needs for human and natural capital, especially for developing countries. Because climate change introduces negative trends and time increasing volatilities both in production and in consumption, social rates of discount can only be estimated within a framework of dynamic uncertainty. For this purpose, climate change can be modeled as a twin stochastic process of the geometric Brownian motion variety, affecting both consumption and productive capacity. Unlike the case of deterministic neoclassical growth, and contrary to the usual estimates for project evaluation, the stochastic nature of climate changes links the social discount rate (SDR) to volatility in two distinct and important ways. On the side of consumption and growth, the SDR is reduced by the likely negative effects of climate change (CC) on growth and food security. It also becomes dependent on the fact that the volatility of growth favors the accumulation of precautionary savings and thus reduces the rate of fall of the value of consumption over time. On the side of production capacity, the SDR is also reduced by the negative effect of CC on the productivity of capital and by the fact that the opportunity cost of the displacement of private investment under dynamic uncertainty is lowered by the value of the options to invest when more information will be available.