Optimal Consumption and Exploration of Nonrenewable Resources Under Uncertainty, Econometrica
Resource consumption yields social utility and exploration effort controls uncertainty in the timings of discoveries as well as their magnitudes. The goal is to maximize the total expected discounted utility of consumtion, net of the exploration effort. We present a controlled storage model and characterize the optimal policy. The associated resource price is shown to follow a stochastic version of the Hotelling.
Sudhakar D. Deshmukh, Stanley R. Pliska
Deshmukh, D. Sudhakar, and Stanley R. Pliska. 1980. Optimal Consumption and Exploration of Nonrenewable Resources Under Uncertainty. Econometrica. 48(1): 177-200.