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This article develops a two-factor real options model of the harvesting decision over infinite rotations assuming a known stochastic price process and using a rigorous Hamilton-Jacobi-Bellman methodology. The harvesting problem is formulated as a linear complementarity problem that is solved numerically using a fully implicit finite difference method. This approach is contrasted with the Markov decision process models commonly used in the literature. The model is used to estimate the value of a representative stand in Ontario's boreal forest, both when there is complete flexibility regarding harvesting time and when regulations dictate the harvesting date. Copyright 2005, Oxford University Press.

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Optimal decisions of a firm facing the option of retrofitting its plant to reduce pollution and thereby eliminate the need to purchase emissions allowances are analysed. The decision is treated as a real option with the price of pollution permits following a known stochastic process. The model is formulated as a set of one-dimensional partial differential equations. At discrete points in time, the firm owner makes optimal decisions about the retrofit, including whether to mothball temporarily. The model is used to analyse a firm's decision to instal a scrubber as a result of the 1990 U.S. Clean Air Act. JEL Classification: Q25, D81, G31Sur la possibilite´d'investir dans le controˆle de la pollution dans un re´gime de permis d'e´mission de pollution e´changeables commercialement. Ce me´moire examine les de´cisions optimales d'une entreprise face a`la possibilite´d'adapter ses installations pour re´duire la pollution, et ce faisant d'e´liminer le besoin de se procurer des permis d'e´mission de pollution sur le marche´. Le de´cision est traite´e comme une option re´elle ou`le prix des permis re´sulte d'un processus stochastique connu. Le mode`le est formule´sous forme d'un ensemble d'e´quations diffe´r-entielles partielles a`une dimension. A des points discontinus dans le temps, le proprie´taire de l'entreprise prend des de´cisions optimales de mise a`niveau des installations -y compris la possibilite´de les fermer temporairement. Le mode`le est utilise´pour analyser une de´cision d'installer un e´purateur suite a`la mise en place de la loi ame´ricaine de 1990 (Clean Air Act).

This paper investigates whether a regime switching model of stochastic lumber prices is better for the analysis of optimal harvesting problems in forestry than a more traditional single regime model. Prices of lumber derivatives are used to calibrate a regime switching model, with each of two regimes characterized by a different mean reverting process. A single regime, mean reverting process is also calibrated. The value of a representative stand of trees and optimal harvesting prices are determined by specifying a Hamilton-JacobiBellman Variational Inequality, which is solved for both pricing models using a fully implicit finite difference approach. The regime switching model is found to more closely match the behaviour of futures prices than the single regime model. In addition, analysis of a tree harvesting problem indicates significant differences in terms of land value and optimal harvest thresholds between the regime switching and single regime models.JEL Classification: C63, C61, Q23, D81

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.

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