Optimal Consumption of a Nonrenewable Resource with Stochastic Discoveries and a Random Environment

We propose a general model of optimal consumtion of a nonrenewable resource under two kinds of uncertainties. One affetcs resource discovery process and the other affects resource supply and demand conditions. The problem is set up as optimal control of a storage process with Markov additive inputs. The optimal value function is characterized and the existence of optimal consumption strategy is established. The optimal consumption rate is shown to be increasing and the resource price decreasing in the level of proven reserves. Several examples are given to illustrate the scope and applicability of the general model