IDEAS home Printed from https://ideas.repec.org/a/eee/forpol/v30y2013icp39-45.html
   My bibliography  Save this article

Faustmann optimal pine stands stochastic rotation problem

Author

Listed:
  • Navarrete, Eduardo
  • Bustos, Jaime

Abstract

The Faustmann optimal rotation harvesting pine stands' models under Logistic and Gompertz wood stock and Brownian price stochastic diffusion processes are reformulated as stochastic one dimensional optimal stopping problem, which are solvable with the Hamilton-Jacobi-Bellman equations. The application of these models to a Chilean forest company stands, shows discrepancies due to the absence of consideration to wood stock and price uncertainties that the company's actual cut policy shows. The stochastic models predict a significant increase of their deterministic optimal cut, with 47.0% and 48.0% in the cases of the Logistical and Gompertz wood stock diffusion respectively. The experimental data significantly validate the Faustmann stochastic logistic model giving a better approximation of the company cut policy, underestimating it by 8.09% and producing a more reliable saturation volume than the Gompertz model. The sensitivity analysis shows that both volatilities have a similar linear effect in the optimal cut, but the wood stock volatility volume elasticity of 0.687 almost double the stumpage price volume elasticity of 0.350, showing the importance of this uncertainty.

Suggested Citation

  • Navarrete, Eduardo & Bustos, Jaime, 2013. "Faustmann optimal pine stands stochastic rotation problem," Forest Policy and Economics, Elsevier, vol. 30(C), pages 39-45.
  • Handle: RePEc:eee:forpol:v:30:y:2013:i:c:p:39-45
    DOI: 10.1016/j.forpol.2013.02.007
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S1389934113000348
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.forpol.2013.02.007?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Willassen, Yngve, 1998. "The stochastic rotation problem: A generalization of Faustmann's formula to stochastic forest growth," Journal of Economic Dynamics and Control, Elsevier, vol. 22(4), pages 573-596, April.
    2. Insley, Margaret, 2002. "A Real Options Approach to the Valuation of a Forestry Investment," Journal of Environmental Economics and Management, Elsevier, vol. 44(3), pages 471-492, November.
    3. 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.
    4. Morck, Randall & Schwartz, Eduardo & Stangeland, David, 1989. "The Valuation of Forestry Resources under Stochastic Prices and Inventories," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 24(4), pages 473-487, December.
    5. Jacco Thijssen, 2010. "Irreversible investment and discounting: an arbitrage pricing approach," Annals of Finance, Springer, vol. 6(3), pages 295-315, July.
    6. Sodal, Sigbjorn, 2002. "The stochastic rotation problem: A comment," Journal of Economic Dynamics and Control, Elsevier, vol. 26(3), pages 509-515, March.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Accastello, Cristian & Blanc, Simone & Mosso, Angela & Brun, Filippo, 2018. "Assessing the timber value: A case study in the Italian Alps," Forest Policy and Economics, Elsevier, vol. 93(C), pages 36-44.
    2. Musshoff, Oliver & Maart-Noelck, Syster Christin, 2014. "An experimental analysis of the behavior of forestry decision-makers — The example of timing in sales decisions," Forest Policy and Economics, Elsevier, vol. 41(C), pages 31-39.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Ben Abdallah, Skander & Lasserre, Pierre, 2016. "Asset retirement with infinitely repeated alternative replacements: Harvest age and species choice in forestry," Journal of Economic Dynamics and Control, Elsevier, vol. 70(C), pages 144-164.
    2. 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.
    3. 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).
    4. 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.
    5. Creamer, Selmin F. & Genz, Alan & Blatner, Keith A., 2012. "The Effect of Fire Risk on the Critical Harvesting Times for Pacific Northwest Douglas-Fir When Carbon Price Is Stochastic," Agricultural and Resource Economics Review, Northeastern Agricultural and Resource Economics Association, vol. 41(3), pages 1-14, December.
    6. 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.
    7. Manley, Bruce & Niquidet, Kurt, 2010. "What is the relevance of option pricing for forest valuation in New Zealand?," Forest Policy and Economics, Elsevier, vol. 12(4), pages 299-307, April.
    8. Insley, M.C. & Wirjanto, T.S., 2010. "Contrasting two approaches in real options valuation: Contingent claims versus dynamic programming," Journal of Forest Economics, Elsevier, vol. 16(2), pages 157-176, April.
    9. Manley, Bruce & Niquidet, Kurt, 2017. "How does real option value compare with Faustmann value when log prices follow fractional Brownian motion?," Forest Policy and Economics, Elsevier, vol. 85(P1), pages 76-84.
    10. Guthrie, Graeme & Kumareswaran, Dinesh, 2003. "Carbon Subsidies and Optimal Forest Management," Working Paper Series 3879, Victoria University of Wellington, The New Zealand Institute for the Study of Competition and Regulation.
    11. Simone Kelly, 2017. "The market premium for the option to close: evidence from Australian gold mining firms," Accounting and Finance, Accounting and Finance Association of Australia and New Zealand, vol. 57(2), pages 511-531, June.
    12. 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).
    13. Ben Abdallah, Skander & Lasserre, Pierre, 2017. "Forest land value and rotation with an alternative land use," Journal of Forest Economics, Elsevier, vol. 29(PB), pages 118-127.
    14. repec:vuw:vuwscr:18975 is not listed on IDEAS
    15. 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.
    16. 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.
    17. Strange, Niels & Jacobsen, Jette Bredahl & Thorsen, Bo Jellesmark, 2019. "Afforestation as a real option with joint production of environmental services," Forest Policy and Economics, Elsevier, vol. 104(C), pages 146-156.
    18. Navarrete, Eduardo, 2012. "Modeling optimal pine stands harvest under stochastic wood stock and price in Chile," Forest Policy and Economics, Elsevier, vol. 15(C), pages 54-59.
    19. Newman, D.H., 2002. "Forestry's golden rule and the development of the optimal forest rotation literature," Journal of Forest Economics, Elsevier, vol. 8(1), pages 5-27.
    20. 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.
    21. Pedro Cosme da Costa Vieira, 2008. "Integrating fire risk into the management of forests," FEP Working Papers 290, Universidade do Porto, Faculdade de Economia do Porto.

    More about this item

    Keywords

    Optimal tree cutting; Faustmann stochastic formula; Logistical diffusion; Operational research;
    All these keywords.

    JEL classification:

    • Q23 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Renewable Resources and Conservation - - - Forestry
    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:forpol:v:30:y:2013:i:c:p:39-45. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/forpol .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.