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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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    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. Nabhani, Abbas & Mardaneh, Elham & Sjølie, Hanne K., 2024. "Multi-objective optimization of forest ecosystem services under uncertainty," Ecological Modelling, Elsevier, vol. 494(C).
    5. 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.
    6. 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.
    7. 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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