On Solving the Multirotational Timber Harvesting Problem with Stochastic Prices: A Linear Complementarity Formulation

Insley, Margaret; Rollins, Kimberly

doi:10.1111/j.1467-8276.2005.00759.x

Cited by 101 publications

(80 citation statements)

References 39 publications

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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%

“…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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Section: Forest Property Dmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Uncertainty in Forest Net Present Value Estimations

Holopainen

Mäkinen

Rasinmäki³

et al. 2010

Forests

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“…In the traditional Ornstein-Uhlenbeck process the variance rate is constant, whereas in Equation (1) the conditional variance of P depends on the level of P , thereby preventing P from becoming negative. This process is suggested in Dixit and Pindyck (1994) and is adopted in Insley and Rollins (2005) and Insley and Lei (2007) to represent lumber prices in an optimal tree harvesting problem. Other optimal harvesting papers to adopt variations on this mean reverting process include Plantinga (1998) andGong (1999).…”

Section: Modeling Commodity Prices: An Overview Of Selected Literaturementioning

confidence: 99%

“…The models we consider are a traditional mean reverting process (TMR) as used in Insley and Rollins (2005) and Insley and Lei (2007) and a regime switching model (the RSMR model) in which the spot price follows potentially two different mean reverting processes. We calibrate the two models using lumber derivatives prices and present evidence as to which can better describe timber prices.…”

Section: Calibration Of Lumber Spot Price Modelsmentioning

confidence: 99%

“…Unfortunately it is difficult to conclude definitively whether the price of any particular commodity is stationary or not. As is noted in Insley and Rollins (2005) many different statistical tests exist, but none has been shown to be uniformly most powerful. The assumption of a price process other than GBM generally requires numerical solution of an optimal tree harvesting problem.…”

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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Uncertainty in Forest Production Planning

Alonso‐Ayuso

Escudero

Guignard

et al. 2011

Wiley Encyclopedia of Operations Research and Management Science

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The forest harvest and road construction planning problem consists fundamentally of managing land designated for timber production and divided into harvest cells. For each time period, the planner must decide which cells to cut and what access roads to build in order to maximize expected net profit under uncertainty in the timber price. By introducing a multistage stochastic mixed 0–1 programming model, the planner is able to make more robust decisions based on a range of timber price scenarios over time, maximizing the expected value subject to the satisfaction of the constraints in all scenarios and satisfying the so‐called nonanticipativity constraints, instead of merely analyzing a single average scenario. A case study is presented based on the Chilean forest property Los Copihues as a proof of concept.

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On Solving the Multirotational Timber Harvesting Problem with Stochastic Prices: A Linear Complementarity Formulation

Cited by 101 publications

References 39 publications

Uncertainty in Forest Net Present Value Estimations

Uncertainty in Forest Net Present Value Estimations

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

Uncertainty in Forest Production Planning

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