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The optimal harvesting problem under price uncertainty: the risk averse case

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  • Bernardo K. Pagnoncelli

    (Escuela de Negocios, Universidad Adolfo Ibáñez)

  • Adriana Piazza

    (Universidad Técnica Federico Santa María)

Abstract

We study the exploitation of a one species, multiple stand forest plantation when timber price is governed by a stochastic process. Our model is a stochastic dynamic program with a weighted mean-risk objective function, and our main risk measure is the Conditional Value-at-Risk. We consider two stochastic processes, geometric Brownian motion and Ornstein–Uhlenbeck: in the first case, we completely characterize the optimal policy for all possible choices of the parameters while in the second, we provide sufficient conditions assuring that harvesting everything available is optimal. In both cases we solve the problem theoretically for every initial condition. We compare our results with the risk neutral framework and generalize our findings to any coherent risk measure that is affine on the current price.

Suggested Citation

  • Bernardo K. Pagnoncelli & Adriana Piazza, 2017. "The optimal harvesting problem under price uncertainty: the risk averse case," Annals of Operations Research, Springer, vol. 258(2), pages 479-502, November.
    • Handle: RePEc:spr:annopr:v:258:y:2017:i:2:d:10.1007_s10479-015-1963-9
    DOI: 10.1007/s10479-015-1963-9
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    References listed on IDEAS

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    1. Andrzej Ruszczynski & Alexander Shapiro, 2004. "Conditional Risk Mappings," Risk and Insurance 0404002, University Library of Munich, Germany, revised 08 Oct 2005.
    2. Kim, Young-Hwan & Bettinger, Pete & Finney, Mark, 2009. "Spatial optimization of the pattern of fuel management activities and subsequent effects on simulated wildfires," European Journal of Operational Research, Elsevier, vol. 197(1), pages 253-265, August.
    3. 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.
    4. Alvarez, Luis H.R. & Koskela, Erkki, 2006. "Does risk aversion accelerate optimal forest rotation under uncertainty?," Journal of Forest Economics, Elsevier, vol. 12(3), pages 171-184, December.
    5. Willem Klein Haneveld & Matthijs Streutker & Maarten Vlerk, 2010. "An ALM model for pension funds using integrated chance constraints," Annals of Operations Research, Springer, vol. 177(1), pages 47-62, June.
    6. Valladão, Davi M. & Veiga, Álvaro & Veiga, Geraldo, 2014. "A multistage linear stochastic programming model for optimal corporate debt management," European Journal of Operational Research, Elsevier, vol. 237(1), pages 303-311.
    7. 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.
    8. 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.
    9. Andy Philpott & Vitor de Matos & Erlon Finardi, 2013. "On Solving Multistage Stochastic Programs with Coherent Risk Measures," Operations Research, INFORMS, vol. 61(4), pages 957-970, August.
    10. Avinash K. Dixit & Robert S. Pindyck, 1994. "Investment under Uncertainty," Economics Books, Princeton University Press, edition 1, number 5474.
    11. 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.
    12. Harry Zheng, 2009. "Efficient frontier of utility and CVaR," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 70(1), pages 129-148, August.
    13. 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.
    14. 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.
    15. 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.
    16. 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.
    17. Yoshimoto, Atsushi & Shoji, Isao, 1998. "Searching for an optimal rotation age for forest stand management under stochastic log prices," European Journal of Operational Research, Elsevier, vol. 105(1), pages 100-112, February.
    18. Alvarez, Luis H.R. & Koskela, Erkki, 2007. "Taxation and rotation age under stochastic forest stand value," Journal of Environmental Economics and Management, Elsevier, vol. 54(1), pages 113-127, July.
    19. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
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    Cited by:

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    2. Yu, Zhihan & Ning, Zhuo & Chang, Wei-Yew & Chang, Sun Joseph & Yang, Hongqiang, 2023. "Optimal harvest decisions for the management of carbon sequestration forests under price uncertainty and risk preferences," Forest Policy and Economics, Elsevier, vol. 151(C).
    3. Bushaj, Sabah & Büyüktahtakın, İ. Esra & Haight, Robert G., 2022. "Risk-averse multi-stage stochastic optimization for surveillance and operations planning of a forest insect infestation," European Journal of Operational Research, Elsevier, vol. 299(3), pages 1094-1110.
    4. Reus, Lorenzo & Pagnoncelli, Bernardo & Armstrong, Margaret, 2019. "Better management of production incidents in mining using multistage stochastic optimization," Resources Policy, Elsevier, vol. 63(C), pages 1-1.

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