Optimal Consumption of a Nonrenewable Resource with Stochastic Discoveries and a Random Environment
建立了一个通用模型，研究在资源发现和经济环境双重不确定性下不可再生资源的最优消费问题，证明了最优消费率随探明储量增加而上升、资源价格随探明储量增加而下降，并给出反例说明更好的环境可能导致更高价格和更低消费率。
We present a general model for the optimal consumption of a nonrenewable resource under two kinds of uncertainties. One source of uncertainty is in the resource discovery process and the other is in the economic environment that affects resource supply and demand conditions, such as exhaustion and development of a substitute. The problem is formulated as one of optimally controlling a storage process with Markov additive discoveries. The optimal value of the resource stock is characterized as the solution of a functional equation and the existence of an optimal consumption policy is established. It is shown that, in a given environment, the optimal consumption rate is increasing and the resource price is decreasing in the level of proven reserves. A counterexample is provided to show that better environments may in fact mean higher prices and lower consumption rates. Finally, a variety of examples is given to illustrate the scope and applicability of the general model.