OPTIMAL EXPLOITATION OF NON-RENEWABLE RESOURCES IN STOCHASTIC ENVIRONMENTS

摘要

This thesis takes some first steps towards examining the intertemporal problem of optimally consuming a non-renewable resource and exploring for new sources of supply in which the size of discovery via exploration is a random variable. The introduction of random size of discovery follows from the assumption that the distribution of the resource is random and the outcome of exploration cannot be predicted precisely. An Ito stochastic differential equation is used to describe the accommodation dynamics of the resource. The issue of resource exhaustion is examined when a territorial limit on exploration is imposed. Responses of an economy to resource exhaustion is discussed. The major contributions of the thesis lies in (1) the derivation of a stochastic analogue of the Hotelling rule in the form of a stochastic differential equation; (2) the investigation of the relationship between unexpected large or small sizes of discovery and the market price of resource under different market structures; and (3) the incorporation of territorial limitation on exploration into a model of random discovery.