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The stochastic Mitra–Wan forestry model: risk neutral and risk averse cases

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  • Adriana Piazza
  • Bernardo Pagnoncelli

Abstract

We extend the classic Mitra and Wan forestry model by assuming that prices follow a geometric Brownian motion. We move one step further in the model with stochastic prices and include risk aversion in the objective function. We prove that, as in the deterministic case, the optimal program is periodic both in the risk neutral and risk averse frameworks, when the benefit function is linear. We find the optimal rotation ages in both stochastic cases and show that they may differ significantly from the deterministic rotation age. In addition, we show how the drift of the price process affects the optimal rotation age and how the degree of risk aversion shortens it. We illustrate our findings for an example of a biomass function and for different values of the model’s parameters. Copyright Springer-Verlag Wien 2015

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  • 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.
    • Handle: RePEc:kap:jeczfn:v:115:y:2015:i:2:p:175-194
    DOI: 10.1007/s00712-014-0414-4
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    Cited by:

    1. Bernardo K. Pagnoncelli & Adriana Piazza, 2017. "The optimal harvesting problem under price uncertainty: the risk averse case," Annals of Operations Research, Springer, vol. 258(2), pages 479-502, November.
    2. Carmen G. Higuera-Chan & J. Adolfo Minjárez-Sosa, 2021. "A Mean Field Approach for Discounted Zero-Sum Games in a Class of Systems of Interacting Objects," Dynamic Games and Applications, Springer, vol. 11(3), pages 512-537, September.
    3. Moriguchi, Kai & Ueki, Tatsuhito & Saito, Masashi, 2020. "Establishing optimal forest harvesting regulation with continuous approximation," Operations Research Perspectives, Elsevier, vol. 7(C).

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    More about this item

    Keywords

    Forestry; Dynamic programming; Risk analysis; Coherent risk measures; Q23; C61; D81;
    All these keywords.

    JEL classification:

    • Q23 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Renewable Resources and Conservation - - - Forestry
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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