The role of stochastic monotonicity in the decision to conserve or harvest old-growth forest




Reed, William J.
Ye, J.J.

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The problem of when, if ever, a stand of old-growth forest should be harvested is formulated as an optimal stopping problem, and a decision rule to maximize the expected present value of amenity services plus timber benefits is found analytically. This solution can be thought of as providing the "correct" way in which cost-benefit analysis should be carried out. Future values of amenity services provided by the standing forest and of timber are considered to be uncertain, and are modelled by Geometric Poisson Jump (GPJ) processes. This specification avoids the ambiguity which arises with Geometric Brownian Motion (GBM) models, as to which form of stochastic integral (Ito or Stratonovich) would be employed, but more importantly allows for monotonic (yet stochastic) processes. It is shown that monotonicity (or lack of it) in the value of amenity services relative to timber values plays an important part in the solution. If amenity values never go down (or never go up) relative to timber values then the certain-equivalence cost-benefit procedure provides the optimal solution, and there is no option value. It is only to the extent that the relative valuations can change direction that the certainty-equivalence procedure becomes sub-optimal and option value arises.



irreversible decisions, uncertainty, option value, cost-benefit analysis, stochastic dynamic programming, Poisson jump processes