The Impact of Stochastic Extraction Cost on the Value of an Exhaustible Resource: An Application to the Alberta Oil Sands

Abstract

The optimal management of a non-renewable resource extraction project is studied when input and output prices follow correlated stochastic processes. The decision problem is specified by two Bellman equations describing the project when it is currently operating or mothballed. Solutions are determined numerically using the Least Squares Monte Carlo methodology. The analysis is applied to an oil sands project which uses natural gas during extracting and upgrading. The paper takes into account the co-movement between crude oil and natural gas prices and proposes two price models: one incorporates a long-run link between the two while the other has no such link. Incorporating a long-run relationship between oil and natural gas prices has a significant effect on the value of the project and its optimal operation and reduces the sensitivity of the project to the natural gas price process.

On an optimal extraction problem with regime switching

“…Recalling that σ i > 0 and λ i > 0, i = 1, 2, let α 1 < α 2 < 0 < α 3 < α 4 be the roots of the fourth-order equation 1…”

“…Indeed, for the stopper it is profitable to stop the process X when its level is sufficiently large (but finite, due to discounting). By (3.20), in the (candidate) continuation region (−∞, x * (y)) the value function should identify with a solution to the ODE 1 2 σ 2 ζ xx (x; y) − ρζ(x; y) = 0, that grows at most linearly when x ↓ −∞ (this last condition is due to the linear structure with respect to x of the expected reward on the right-hand side of (3.19)). Hence, ζ(x; y) = A(y) exp(( √ 2ρ/σ )x) for some A(y) > 0 to be determined.…”

“…If the system is reflected at the upper boundary at a time of regime switch, ν * prescribes an immediate jump of Y * from the upper to the lower boundary (whenever they are different). This plot was obtained using MATLAB ® to solve the nonlinear system (3.14) when f (y) = 1 3 (e y − 1) and with σ 1 = 0.38, σ 2 = 1.9, λ 1 = 1.7, λ 2 = 0.44, ρ = 1 3 , and c = 1 2 .…”

“…[11] and [34] and the references therein); in some as a combined absolutely continuous/impulse stochastic control problem (see, e.g. [5] and [23]); and in others as a stochastic optimal control problem only with classical absolutely continuous controls (see [1] and [12], among many others), but with commodity price dynamics possibly described by a Markov regime switching model (see, e.g. [21]).…”

Economic decision making of renewable power producers under uncertainty

“…As for the stochastic O&M costs, Khoub Bakht et al (2008) investigates statistical repair and maintenance cost models for tractors while Leung and Lai (2003) statistically studied the quality and reliability aspects of bus engines. Almansour and Insley (2011), on the other hand, applies the stochastic cost model for the oil sands in Canada. In addition, in Costa Lima and Suslick (2006), both the price and operating costs are modeled as GBM processes for mining projects.…”