A martingale characterization of the price of a nonrenewable resource with decisions involving uncertainty
Abstract This paper presents a general model of nonrenewable resource consumption and exploration decisions involving uncertainty about the time of occurrence of an event such as exhaustion, stock discovery, or a substitute development. The resulting price process is characterized in terms of necessary and sufficient conditions under which the price is expected to rise at a rate equal to, greater than, or less than the discount rate. The general model is illustrated and the price process and the optimal decisions are characterized by examining the three types of uncertainty indicated above.