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Further generalization of Faustmann's formula for stochastic interest rates

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  • Buongiorno, Joseph
  • Zhou, Mo

Abstract

Markov decision process (MDP) models generalize Faustmann's formula by recognizing that future stand states, prices, and interest rates, are not known exactly. Buongiorno (Forest Science 47(4) 2001) presents a dynamic programming and a linear programming formulation of the MDP model with a fixed interest rate. Both formulations are generalized here to account for a stochastic interest rate. The objective function is the expected present value of returns over an infinite horizon. It gives, like Faustmann's formula, the value of the land and the eventual standing trees. The changes between stand states, prices, and interest rate, are represented by Markov chains. Faustmann's formula is a special case where the change from one state to another has 0 or 1 probability, and the interest rate is constant. The MDP model applies to any stand state, even- or uneven-aged, and the best decisions are tied uniquely to the current system state. An example shows the effects of recognizing variations in interest rate on the land expectation value, and the cost of ignoring them.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:foreco:v:17:y:2011:i:3:p:248-257
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    Cited by:

    1. Couture, Stéphane & Cros, Marie-Josée & Sabbadin, Régis, 2016. "Risk aversion and optimal management of an uneven-aged forest under risk of windthrow: A Markov decision process approach," Journal of Forest Economics, Elsevier, vol. 25(C), pages 94-114.
    2. Bastit, Félix & Brunette, Marielle & Montagné-Huck, Claire, 2023. "Pests, wind and fire: A multi-hazard risk review for natural disturbances in forests," Ecological Economics, Elsevier, vol. 205(C).
    3. Stéphane S. Couture & Marie-Josée Cros & Régis Sabbadin, 2014. "Risk preferences and optimal management of uneven-aged forests in the presence of climate change: a Markov decision process approach," Post-Print hal-02741407, HAL.
    4. Sylvain Caurla & Antonello Lobianco, 2020. "Estimating climate service value in forestry : The case of climate information on drought for maritime pine in Southwestern France," Post-Print hal-03639335, HAL.
    5. Müller, Fabian & Hanewinkel, Marc, 2018. "Challenging the assumptions of a standard model: How historical triggers in terms of technical innovations, labor costs and timber price change the land expectation value," Forest Policy and Economics, Elsevier, vol. 95(C), pages 46-56.
    6. Petri P Kärenlampi, 2019. "Wealth accumulation in rotation forestry – Failure of the net present value optimization?," PLOS ONE, Public Library of Science, vol. 14(10), pages 1-19, October.
    7. Sylvain Caurla & Antonello Lobianco, 2020. "Estimating climate service value in forestry : The case of climate information on drought for maritime pine in Southwestern France," Post-Print hal-02617889, HAL.
    8. Zhou, Mo, 2015. "Adapting sustainable forest management to climate policy uncertainty: A conceptual framework," Forest Policy and Economics, Elsevier, vol. 59(C), pages 66-74.

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