Optimal Harvest Policy with First-Order Autoregressive Price Process

The optimal harvest decision policy for even-aged stand management when timber price follows a first-order autoregressive process is investigated. It is proved that the expected present value of an even-aged stand at any age is an increasing and convex function of the timber price in the previous year, provided that the maximum age the stand is allowed to grow is sufficiently high. The optimal decision rule at each age depends on the current annual timber growth, the price autocorrelation coefficient, and the discount rate. A critical annual timber growth rate is defined by the timber price autocorrelation coefficient and the discount rate. When stand age is low such that the annual growth rate is higher than this critical rate, it is optimal either to wait independent of the observed price or to harvest the stand when the observed price is relatively low. At higher ages when the annual timber growth rate is lower than the critical rate, there exists an age-dependent reservation price and it is optimal to harvest when the observed price is equal to or greater than the reservation price. The optimal harvest policy when timber price process is random walk has similar properties. A simulation methodfor determining the optimal decision rules is developed. The effects of price autocorrelation coefficient on the optimal harvest policy and on the expected gain of adaptive decision making are examined using an example.