Faustmann Optimal Pine Stands Stochastic Rotation Problem

Eduardo Navarrete, Jaime Bustos

Abstract

The Faustmann optimal rotation harvesting pine stands models under Logistic and Gompertz wood stock and Brown price stochastic diffusion processes are reformulated as stochastic one dimensional optimal stopping problem, which are solvable with the Hamilton-Jacobi-Bellman equations. The stochastic models predict a significant increase of the deterministic optimal cut, with 47.0% and 48.0% in the cases of the Logistical and Gompertz wood stock diffusion respectively. The application of these models to a Chilean forest company shows discrepancies due to the absence of consideration to wood stock and price uncertainties that the company actual cut policy shows. The experimental data significantly validate the Faustmann stochastic logistic model. They give 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 doubles the stumpage price volume elasticity of 0.350, showing the importance of this uncertainty.

References

  1. Alvarez L. R., Koskela E., 2007. Optimal Harvesting under Resource Stock and Price Uncertainty, Journal of Economics Dynamics & Control, Vol. 31 , Issue 7, pp. 2461-2485.
  2. Beskos A., Papaspliopoulos O., Roberts G., 2006. Exact computationally efficient likelihood-based estimation for discretely observed diffusion, J. Statist.Soc. B,68Part2, pp1-29.
  3. Clark R., Reed W., 1989. The Tree Cutting Problem in a Stochastic Environment, Journal of Economics Dynamics and Control, N° 13. 569-595.
  4. Faustmann M., 1995, (Originally,1849). Calculation of the Value which Forest Land and Immature Stands Processess for Forestry, Journal of Forest Economics Vol.1: pp.7-44.
  5. Garcia O., 2005. Unifying Sigmoid Univariate Growth Equations, FBMIS.
  6. Gutierrez R.,Gutierrez-Sanchez , Nafidi A:, 2008. Modelling and forecasting vehicle stocks using trends of stochastic Gompertz diffusion models, Appl.Stochastic Model Bus.Ind., 25,:385.
  7. Insley M., (2002). “A Real Option Approach to the Valuation of a Forestry on Investment,” Journal of Environmental Economics and Management. Vol. 44, 471-492
  8. Insley M., Rollins K., 2005. On solving the multirotational timber harvesting problem with stochastic prices: a linear complimentarily formulation. American Journal of Agriculture Economics.Vol87, N 3, pp. 735-755.
  9. Jacco,J. J.,Thijssen, 2010. Irreversible Investment and discounting: an arbitrage pricing approach, Annals of Finance, Volume 6, Number 3, 295-315.
  10. Johnson T.C., 2006. The optimal Timing of Investment Decisions, PhD thesis, University of London.
  11. Kloeden P., Platen E., 1991. Numerical Solution of Stochastic Differential Equation, page 125, SpringerVerlag Berlin
  12. Meyer P., Yung J., Ausubel J., 1999. A primer on Logistic Growth and Substitution: The Mathematics of the Logolet Lab Software, Technological Foresting and Social Change.
  13. Morck, R., E. Schwartz, 1989. The valuation of Forestry Resources under Stochastic Prices and Inventories, J. Financial and Quantitative Analysis.Vol. 24, pp 473- 487.
  14. Navarrete E., 2011. Modelling Optimal Pine Stands Harvest under Stochastic Wood Stock and Price in Chile, Journal of Forest Policy and Economics, Doi:10.1016/j.forpol.2011.09.005.
  15. Oksendal, B., 2000. Stochastic Differential Equations, (Fith Ed.) Springer Verlag.
  16. Samuelson P., 1976. Economics of Forestry in an evolving Economy, Economic Inquiry Vol.14, pp. 466-491
  17. Willassen Y., 1998. The stochastic rotation problem: a generalization of FaustmanÀs formula to a stochastic forest growth, Journal of Economics Dynamics & Control. 22, 573-596.
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Paper Citation


in Harvard Style

Navarrete E. and Bustos J. (2013). Faustmann Optimal Pine Stands Stochastic Rotation Problem . In Proceedings of the 2nd International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES, ISBN 978-989-8565-40-2, pages 205-212. DOI: 10.5220/0004285402050212


in Bibtex Style

@conference{icores13,
author={Eduardo Navarrete and Jaime Bustos},
title={Faustmann Optimal Pine Stands Stochastic Rotation Problem},
booktitle={Proceedings of the 2nd International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,},
year={2013},
pages={205-212},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0004285402050212},
isbn={978-989-8565-40-2},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 2nd International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,
TI - Faustmann Optimal Pine Stands Stochastic Rotation Problem
SN - 978-989-8565-40-2
AU - Navarrete E.
AU - Bustos J.
PY - 2013
SP - 205
EP - 212
DO - 10.5220/0004285402050212