A General Approach to the Stochastic Rotation Problem with Amenity Valuation

This paper presents a new and general approach to study the optimal rotation policy with amenity valuation under uncertainty. We first postulate the stochastic forest value and assume plausibly that monetary value of amenities is a continuous and non-negative function of forest value thus presenting the trade-off between timber revenues and amenity values. Second, instead of using a dynamic programming approach, we derive an iterative representation of the total forest value and solve the optimal rotation threshold by applying ordinary non-linear programming techniques. Third, we characterize how under certain set of conditions the properties of both the expected cumulative value and the expected marginal cumulative value, accrued from amenity services, depend on the precise nature of the monetary valuation of amenities and how increased forest value volatility affects these concepts. Finally, after new theoretical characterizations we illustrate our results numerically in the Wicksellian single rotation and Faustmannian ongoing rotation frameworks. We show that in contrast to the current literature the impact of volatility on the Faustmannian rotation threshold might be positive or negative depending on the precise nature of amenity valuation function.