Optimal costless extraction rate changes from a non-renewable resource

Abstract

This paper considers the role of costless decisions relating to the extraction of a non-renewable resource in the presence of uncertainty. We begin by deriving a size scale of the extractable resource, above which the solution to the valuation and optimal control strategy can be described by analytic solutions; we produce solutions for a general form of operating cost function. Below this critical resource size level the valuation and optimal control strategy must be solved by numerical means; we present a robust numerical algorithm that can solve such a class of problem. We also allow for the embedding of an irreversible investment decision (abandonment) into the optimisation. Finally, we conduct experimentation for each of these two approaches (analytical and numerical), and show how they are consistent with one another when used appropriately. The extensions of this paper's techniques to renewable resources are explored.

Stochastic differential game for management of non-renewable fishery resource under model ambiguity

“…We guess the solution to the reduced HJBI equation (13) having the form = x 1−αẑ (18) with a constantẑ > 0. The ansatz is based on the functional form of the performance index φ and the formal linearity of the SDE (2) (g = r) with respect to X t .…”

“…The ansatz is based on the functional form of the performance index φ and the formal linearity of the SDE (2) (g = r) with respect to X t . Under the stated assumptions, substituting (18) into (13) shows that the solution of the form (18) exists and is unique if z =ẑ > 0 solves…”

“…Analysis of in (18) thus reduces to analysis of the parameter dependence of the coefficientẑ. The following proposition holds for the coefficientẑ as a function of the parameters.…”

“…The above-mentioned previous papers did not simultaneously address qualitative analysis and numerical analysis, while the present mathematical analysis is both qualitative and quantitative since it is exactly solvable, and at least partly supports their results theoretically. Although not a research on fishery management, Evatt et al [18] numerically showed for a non-renewable resource extraction problem that increasing the parameter σ results in a decreased total profit as in Proposition 3.3. The computational results presented in the next section quantify the fishery resources management under different environmental conditions.…”

“…Non-renewability of the population distinguishes the present model from the conventional ones for renewable resources. Several researchers have approached optimal management of non-renewable resources from social and economic viewpoints indicating their high importance [3,16,18,35,37,50,63].…”