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Optimal harvesting under resource stock and price uncertainty

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  • Alvarez, Luis H.R.
  • Koskela, Erkki

Abstract

We analyze optimal harvesting policy under stochastic price and stock dynamics. We state a set of weak conditions under which the optimal policy can be characterized by a single exercise threshold and show that the value of optimal harvesting and depletion policies can be expressed as the separable form according to which only the current price and the expected per capita growth rate affect the threshold, while under risk neutrality volatility of price dynamics will have no effect. Uncertainty makes waiting valuable and the optimal threshold is higher when harvesting can be exercised only once than in the sequential case.
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  • Alvarez, Luis H.R. & Koskela, Erkki, 2007. "Optimal harvesting under resource stock and price uncertainty," Journal of Economic Dynamics and Control, Elsevier, vol. 31(7), pages 2461-2485, July.
    • Handle: RePEc:eee:dyncon:v:31:y:2007:i:7:p:2461-2485
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    3. Coculescu, Delia, 2011. "Dividends and leverage: How to optimally exploit a non-renewable investment," Journal of Economic Dynamics and Control, Elsevier, vol. 35(3), pages 312-329, March.
    4. Navarrete, Eduardo & Bustos, Jaime, 2013. "Faustmann optimal pine stands stochastic rotation problem," Forest Policy and Economics, Elsevier, vol. 30(C), pages 39-45.
    5. Neha Deopa & Daniele Rinaldo, 2020. "Quickest Detection of Ecological Regimes for Natural Resource Management," Papers 2005.11500, arXiv.org, revised Mar 2024.
    6. Neha Deopa & Daniele Rinaldo, 2024. "Quickest Detection of Ecological Regimes for Natural Resource Management," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 87(5), pages 1327-1366, May.
    7. Mike Ludkovski, 2022. "Regression Monte Carlo for Impulse Control," Papers 2203.06539, arXiv.org.
    8. Tahvonen, Olli & Suominen, Antti & Malo, Pekka & Viitasaari, Lauri & Parkatti, Vesa-Pekka, 2022. "Optimizing high-dimensional stochastic forestry via reinforcement learning," Journal of Economic Dynamics and Control, Elsevier, vol. 145(C).
    9. Davis, Graham A. & Cairns, Robert D., 2012. "Good timing: The economics of optimal stopping," Journal of Economic Dynamics and Control, Elsevier, vol. 36(2), pages 255-265.
    10. 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.
    11. Pekka Matomäki, 2012. "On solvability of a two-sided singular control problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 76(3), pages 239-271, December.
    12. Chang, Sun Joseph & Zhang, Fan, 2023. "Active timber management by outsourcing stumpage price uncertainty with the American put option," Forest Policy and Economics, Elsevier, vol. 154(C).
    13. Framstad, Nils Chr., 2014. "The Effect of Small Intervention Costs on the Optimal Extraction of Dividends and Renewable Resources in a Jump-Diffusion Model," Memorandum 25/2014, Oslo University, Department of Economics.
    14. Buongiorno, Joseph & Zhou, Mo, 2011. "Further generalization of Faustmann's formula for stochastic interest rates," Journal of Forest Economics, Elsevier, vol. 17(3), pages 248-257, August.
    15. Guo, Christopher & Costello, Christopher, 2013. "The value of adaption: Climate change and timberland management," Journal of Environmental Economics and Management, Elsevier, vol. 65(3), pages 452-468.
    16. Chang, Sun Joseph, 2020. "Twenty one years after the publication of the generalized Faustmann formula," Forest Policy and Economics, Elsevier, vol. 118(C).
    17. Hening, A. & Tran, K. Q. & Ungureanu, S., 2021. "The Effects of Random and Seasonal Environmental Fluctuations on Optimal Harvesting and Stocking," Working Papers 21/05, Department of Economics, City University London.
    18. Holopainen, Markus & Mäkinen, Antti & Rasinmäki, Jussi & Hyytiäinen, Kari & Bayazidi, Saeed & Pietilä, Ilona, 2010. "Comparison of various sources of uncertainty in stand-level net present value estimates," Forest Policy and Economics, Elsevier, vol. 12(5), pages 377-386, June.
    19. Chladna, Zuzana, 2007. "Determination of optimal rotation period under stochastic wood and carbon prices," Forest Policy and Economics, Elsevier, vol. 9(8), pages 1031-1045, May.

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