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Further generalization of Faustmann's formula for stochastic interest rates

  • Buongiorno, Joseph
  • Zhou, Mo
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    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.

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    Article provided by Elsevier in its journal Journal of Forest Economics.

    Volume (Year): 17 (2011)
    Issue (Month): 3 (August)
    Pages: 248-257

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    Handle: RePEc:eee:foreco:v:17:y:2011:i:3:p:248-257
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    1. 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.
    2. Ching-Rong Lin & Joseph Buongiorno, 1998. "Tree Diversity, Landscape Diversity, and Economics of Maple-Birch Forests: Implications of Markovian Models," Management Science, INFORMS, vol. 44(10), pages 1351-1366, October.
    3. Luis H. R. Alvarez & Erkki Koskela, 2005. "Optimal Harvesting under Resource Stock and Price Uncertainty," CESifo Working Paper Series 1384, CESifo Group Munich.
    4. Miller, Robert A. & Voltaire, Karl, 1980. "A sequential stochastic tree problem," Economics Letters, Elsevier, vol. 5(2), pages 135-140.
    5. 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.
    6. repec:ltr:wpaper:1989.01 is not listed on IDEAS
    7. Alvarez, Luis H R & Koskela, Erkki, 2003. "On Forest Rotation under Interest Rate Variability," International Tax and Public Finance, Springer, vol. 10(4), pages 489-503, August.
    8. Harry R Clarke & William J. Reed, 1989. "The Tree-Cutting Problem in a Stochastic Environment: The case of Age Dependent Growth," Working Papers 1989.01, School of Economics, La Trobe University.
    9. Miller, Robert A. & Voltaire, Karl, 1983. "A stochastic analysis of the tree paradigm," Journal of Economic Dynamics and Control, Elsevier, vol. 6(1), pages 371-386, September.
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