The Forest Rotation Problem With Stochastic Harvest and Amenity Value

Abstract

ABSTRACT. We present a general approach to study optimal rotation policy with amenity valuationunder stochastic forest stand value. We state a set of weak conditions under which a unique optimal harvesting threshold exists and derive the value of the optimal policy. We characterize the impact of forest stand value volatility on both the total and the marginal expected cumulative present value of the revenues accrued from amenities. We also illustrate our results numerically and find that depending on the precise characteristics of amenity valuation higher forest stand value volatility may accelerate the rotation policy by decreasing the optimal harvesting threshold.

A review of decision-making approaches to handle uncertainty and risk in adaptive forest management under climate change

“…5). Amenity was also included in a considerable part of the literature (16%) compared with other objectives (Pukkala and Miina 1997;Prato 2000;Bulte et al 2002;Alvarez and Koskela 2007a;Zhou et al 2008). However, non-timber products and services like biodiversity, carbon, wildlife and water were only considered in a smaller number of studies Decision-making to handle climate change (Huang et al 1998;Creedy and Wurzbacher 2001;Bulte et al 2002;Spring et al 2008;Galik and Jackson 2009;Yousefpour 2009), which made up 9%, 8% and 6% of the papers.…”

Bounded Variation Control of Itô Diffusions with Exogenously Restricted Intervention Times

“…Since ϕ r+λ (x) < 0 and g (x)ψ r (x) < g (x)ψ r (x), and by using Corollary 2 for the function ψ r (this is justified by (7)), the resolvent equation (2), and Lemma 3, we have…”

The forest harvesting problem: have we reached the limit of our understanding?

“…The Faustmann rotation age in some cases can even be relevant to uneven-aged forest or multiple crop models (Wan 1994, Chang 1998, Haight 1987. One prolific area of research has been to investigate the optimality of the Faustmann rotation age when there is risk of natural/catastrophic events or future timber prices (Reed 1984, Brazee and Mendelsohn 1988, Plantinga 1998, Gong 1998 and additionally risk averse landowners (Alvarez and Koskela 2007, Lien et al 2007, Zhang 2001, Clarke and Reed 1989. There are in fact also Faustmann-like solutions in stochastic harvest stopping problems where prices or forest stocks evolve over time according to known drift and volatility (F. Chang 2005, Sodal 2002, Willassen 1998).…”

“…Amenities to a lesser extent have been introduced in problems with stochastic market parameters, and a few articles consider stochastic amenities themselves (Gong et al 2005, Reed, 1993, Conrad 1997, Alvarez and Koskela 2007. And of course, because amenities can be defined as public goods, and a landowner would not be expected to have identical preferences to a social decision maker, Hartman type rotation models have been instrumental in defining the nature of externalities and social costs involving forests, with a wide range of applications including deforestation, forest taxation and subsidy design, biodiversity, and carbon storage.…”