Stochastic control modeling for forest stand management under uncertain price dynamics through geometric brownian motion

In this paper, a stochastic control model is constructed by incorporating geometric Brownian motion to capture uncertain price dynamics into a one-stage and two-state stochastic dynamic programming model. The proposed model is designed to search for optimal harvest timing under price uncertainty without considering other forestry operations,e.g., thinning. We consider the option of abandoning forest management for an alternative use of forest land besides replantation. Our experimental analysis shows that the optimal harvest timing under stochastic log prices is delayed when a price level is crucially low for maintaining the management. It is also shown that when the current log price is sufficiently high, the optimal harvest timing derived from both the stochastic and deterministic approach becomes the same. With a downward trend of stochastic price dynamics, the optimal harvest timing tends to be hastened overall. This is because of the depreciation effect on the future return, which stimulates harvesting in an earlier period. This research was supported by a Grant-in-Aid for Scientific Research (No.11660155) from the Ministry of Education, Culture, Sports, Science and Technology of Japan.