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The optimal harvesting problem under price uncertainty

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  • Adriana Piazza
  • Bernardo Pagnoncelli

Abstract

In this paper we study the exploitation of a one species forest plantation when timber price is governed by a stochastic process. The work focuses on providing closed expressions for the optimal harvesting policy in terms of the parameters of the price process and the discount factor, with finite and infinite time horizon. We assume that harvest is restricted to mature trees older than a certain age and that growth and natural mortality after maturity are neglected. We use stochastic dynamic programming techniques to characterize the optimal policy and we model price using a geometric Brownian motion and an Ornstein–Uhlenbeck process. In the first case we completely characterize the optimal policy for all possible choices of the parameters. In the second case we provide sufficient conditions, based on explicit expressions for reservation prices, assuring that harvesting everything available is optimal. In addition, for the Ornstein–Uhlenbeck case we propose a policy based on a reservation price that performs well in numerical simulations. In both cases we solve the problem for every initial condition and the best policy is obtained endogenously, that is, without imposing any ad hoc restrictions such as maximum sustained yield or convergence to a predefined final state. Copyright Springer Science+Business Media New York 2014

Suggested Citation

  • Adriana Piazza & Bernardo Pagnoncelli, 2014. "The optimal harvesting problem under price uncertainty," Annals of Operations Research, Springer, vol. 217(1), pages 425-445, June.
    • Handle: RePEc:spr:annopr:v:217:y:2014:i:1:p:425-445:10.1007/s10479-014-1559-9
    DOI: 10.1007/s10479-014-1559-9
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    1. Clarke, Harry R. & Reed, William J., 1989. "The tree-cutting problem in a stochastic environment : The case of age-dependent growth," Journal of Economic Dynamics and Control, Elsevier, vol. 13(4), pages 569-595, October.
    2. Peter Lohmander, 2000. "Optimal sequential forestry decisions under risk," Annals of Operations Research, Springer, vol. 95(1), pages 217-228, January.
    3. Tapan Mitra & Henry Y. Wan, 1985. "Some Theoretical Results on the Economics of Forestry," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 52(2), pages 263-282.
    4. Jose Mosquera & Mordecai Henig & Andres Weintraub, 2011. "Design of insurance contracts using stochastic programming in forestry planning," Annals of Operations Research, Springer, vol. 190(1), pages 117-130, October.
    5. Salo, Seppo & Tahvonen, Olli, 2002. "On Equilibrium Cycles and Normal Forests in Optimal Harvesting of Tree Vintages," Journal of Environmental Economics and Management, Elsevier, vol. 44(1), pages 1-22, July.
    6. Margaret Insley & Kimberly Rollins, 2005. "On Solving the Multirotational Timber Harvesting Problem with Stochastic Prices: A Linear Complementarity Formulation," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 87(3), pages 735-755.
    7. Thomas A. Thomson, 1992. "Optimal Forest Rotation When Stumpage Prices Follow a Diffusion Process," Land Economics, University of Wisconsin Press, vol. 68(3), pages 329-342.
    8. Bruce McGough & Andrew J. Plantinga & Bill Provencher, 2004. "The Dynamic Behavior of Efficient Timber Prices," Land Economics, University of Wisconsin Press, vol. 80(1), pages 95-108.
    9. Alvarez, Luis H. R. & Koskela, Erkki, 2005. "Wicksellian theory of forest rotation under interest rate variability," Journal of Economic Dynamics and Control, Elsevier, vol. 29(3), pages 529-545, March.
    10. Olli Tahvonen, 2004. "Optimal Harvesting Of Forest Age Classes: A Survey Of Some Recent Results," Mathematical Population Studies, Taylor & Francis Journals, vol. 11(3-4), pages 205-232.
    11. Antonio Alonso-Ayuso & Laureano Escudero & Monique Guignard & Martín Quinteros & Andres Weintraub, 2011. "Forestry management under uncertainty," Annals of Operations Research, Springer, vol. 190(1), pages 17-39, October.
    12. Gjolberg, Ole & Guttormsen, Atle G., 2002. "Real options in the forest: what if prices are mean-reverting?," Forest Policy and Economics, Elsevier, vol. 4(1), pages 13-20, May.
    13. Avinash K. Dixit & Robert S. Pindyck, 1994. "Investment under Uncertainty," Economics Books, Princeton University Press, edition 1, number 5474.
    14. Bastian-Pinto, Carlos & Brando, Luiz & Hahn, Warren J., 2009. "Flexibility as a source of value in the production of alternative fuels: The ethanol case," Energy Economics, Elsevier, vol. 31(3), pages 411-422, May.
    15. Laurence Reeves & Robert Haight, 2000. "Timber harvest scheduling with price uncertainty using Markowitz portfolio optimization," Annals of Operations Research, Springer, vol. 95(1), pages 229-250, January.
    16. Roberto Cominetti & Adriana Piazza, 2009. "Asymptotic Convergence of Optimal Policies for Resource Management with Application to Harvesting of Multiple Species Forest," Mathematics of Operations Research, INFORMS, vol. 34(3), pages 576-593, August.
    17. Salo, Seppo & Tahvonen, Olli, 2003. "On the economics of forest vintages," Journal of Economic Dynamics and Control, Elsevier, vol. 27(8), pages 1411-1435, June.
    18. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
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    2. Miguel A. Lejeune & Janne Kettunen, 2017. "Managing Reliability and Stability Risks in Forest Harvesting," Manufacturing & Service Operations Management, INFORMS, vol. 19(4), pages 620-638, October.
    3. Miguel A. Lejeune & Janne Kettunen, 2018. "A fractional stochastic integer programming problem for reliability-to-stability ratio in forest harvesting," Computational Management Science, Springer, vol. 15(3), pages 583-597, October.
    4. Adriana Piazza & Bernardo Pagnoncelli, 2015. "The stochastic Mitra–Wan forestry model: risk neutral and risk averse cases," Journal of Economics, Springer, vol. 115(2), pages 175-194, June.
    5. Ignacio Rios & Andres Weintraub & Roger J.-B. Wets, 2016. "Building a stochastic programming model from scratch: a harvesting management example," Quantitative Finance, Taylor & Francis Journals, vol. 16(2), pages 189-199, February.
    6. Khan, M. Ali, 2016. "On a forest as a commodity and on commodification in the discipline of forestry," Forest Policy and Economics, Elsevier, vol. 72(C), pages 7-17.

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