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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