The tree-cutting problem in a stochastic environment

Clarke, Harry; Reed, William J.

doi:10.1016/0165-1889(89)90004-3

Cited by 153 publications

(117 citation statements)

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“…In the literature on optimal tree harvesting, early papers adopting the GBM assumption include Reed and Clarke (1990), Clarke and Reed (1989), Yin and Newman (1995), and Morck et al (1989).…”

Section: Modeling Commodity Prices: An Overview Of Selected Literaturementioning

confidence: 99%

“…An ongoing challenge is how best to model the dynamics of timber prices in determining optimal harvesting strategies and in estimating the value of forested lands. Over the past two decades some researchers have modeled price as an exogenous factor described by a stochastic differential equation (see Thomson (1992); Plantinga (1998); Morck et al (1989); Clarke and Reed (1989) for example). Others have used stand value (price of wood times quantity of wood), as the stochastic factor, abstracting from physical tree growth, such as in Alvarez and Koskela (2007) and Alvarez and Koskela (2005).…”

Section: Introductionmentioning

confidence: 99%

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Regime switching in stochastic models of commodity prices: An application to an optimal tree harvesting problem

Shan

Insley

2012

Journal of Economic Dynamics and Control

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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

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Section: Modeling Commodity Prices: An Overview Of Selected Literaturementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Regime switching in stochastic models of commodity prices: An application to an optimal tree harvesting problem

Shan

Insley

2012

Journal of Economic Dynamics and Control

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“…The price uncertainty is likely to increase when using e.g., GBM [35][36][37] instead of GMR [32][33][34] as process for future price increments. The increasing price variation increases also the degree of yield value prediction uncertainty.…”

Section: Forest Property Dmentioning

confidence: 99%

“…The reservation price may therefore vary among stands. Several studies (e.g., [35,[54][55][56]) have shown that following the use of minimum prices, forestry net yields have increased markedly.…”

Section: Forest Property Dmentioning

confidence: 99%

“…A more advanced, and also complicated, approach is to try to predict future timber price development based on realized past price development, by which long-term trends can be depicted and factors causing price peaks identified. Such predictions can be carried out e.g., by using geometric mean-reverting (GMR, [32][33][34]) or geometric Brownian motion (GBM, [35][36][37]) price processes.…”

Section: Introductionmentioning

confidence: 99%

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Uncertainty in Forest Net Present Value Estimations

Holopainen

Mäkinen

Rasinmäki³

et al. 2010

Forests

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Uncertainty related to inventory data, growth models and timber price fluctuation was investigated in the assessment of forest property net present value (NPV). The degree of uncertainty associated with inventory data was obtained from previous area-based airborne laser scanning (ALS) inventory studies. The study was performed, applying the Monte Carlo simulation, using stand-level growth and yield projection models and three alternative rates of interest (3, 4 and 5%). Timber price fluctuation was portrayed with geometric mean-reverting (GMR) price models. The analysis was conducted for four alternative forest properties having varying compartment structures: (A) a property having an even development class distribution, (B) sapling stands, (C) young thinning stands, and (D) mature stands. Simulations resulted in predicted yield value (predicted NPV) distributions at both stand and property levels. Our results showed that ALS inventory errors were the most prominent source of uncertainty, leading to a 5.1-7.5% relative deviation of property-level NPV when an interest rate of 3% was applied. Interestingly, ALS inventory led to significant biases at the property level, ranging from 8.9% to 14.1% (3% interest rate). ALS inventory-based bias was the most significant in mature stand properties. Errors related to the growth predictions led to a relative standard deviation in NPV, varying from 1.5% to 4.1%. Growth model-related uncertainty was most significant OPEN ACCESSForests 2010, 1 178 in sapling stand properties. Timber price fluctuation caused the relative standard deviations ranged from 3.4% to 6.4% (3% interest rate). The combined relative variation caused by inventory errors, growth model errors and timber price fluctuation varied, depending on the property type and applied rates of interest, from 6.4% to 12.6%. By applying the methodology described here, one may take into account the effects of various uncertainty factors in the prediction of forest yield value and to supply the output results with levels of confidence.

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The Effect of Catastrophic Risk on Forest Investment Decisions

Yin

Newman

1996

Journal of Environmental Economics and Management

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The tree-cutting problem in a stochastic environment

Cited by 153 publications

References 15 publications

Regime switching in stochastic models of commodity prices: An application to an optimal tree harvesting problem

Regime switching in stochastic models of commodity prices: An application to an optimal tree harvesting problem

Uncertainty in Forest Net Present Value Estimations

The Effect of Catastrophic Risk on Forest Investment Decisions

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