A Comparative Analysis of A Stochastic Control Model based on Mean-Reverting Process for Forest Stand Management

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Other Title
  • Mean-Reverting過程による林分経営最適確率制御モデルの比較分析

Abstract

<p>A stochastic model for log price dynamics was provided with use of a variant of mean-reverting process, in which the drift term was a linear function of price and the volatility term was a function of price as in that of geometric Brownian motion. By approximating this stochastic model by the binomial process, we constructed a stochastic control model for forest stand management. The proposed control model was to select an optimal decision from three controls, "Harvest-Plantation", "Harvest-Abandon", and "Wait for Harvesting" under price stochasticity. The forest stand growth was derived from the stand density management diagram in the Kyushu region, following the standard forestry practice manual. Using the monthly time series data of sugi (Cryptomeria japonica) log price from 1975 to 2000, our analyses showed that the proposed mean-reverting process outperformed geometric Brownian motion most based on AIC for the time series data from September of 1980 to April of 1991. The resultant reverted mean became around 26,000 Yen/m3. As for the corresponding optimal rotation age, it was showed that if the current log price was lower than the resultant reverted mean, the rotation was postponed forever due to the large degree of expectation of price increase over time. On the other hand, if the current price was above the reverted mean, the rotation age became longer as the current price approached to the reverted mean.</p>

Journal

  • FORMATH

    FORMATH 5 (0), 85-104, 2006

    FORMATH Research Society

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