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Alvarez, Luis H. R., Koskela, Erkki 2002. Wicksellian Theory of Forest Rotation under Interest Rate Variability. PTT working papers 62.
Abstract: The current literature on optimal forest rotation makes the assumption of constant interest rate. However, the irreversible harvesting decisions of forest stands are typically subject to relatively long time horizons over which interest rate do ﬂuctuate. In this paper we apply the Wicksellian single rotation framework to extend the existing studies to cover the unexplored case of variable and stochastic interest rate. Given the technical generality of the considered valuation problem, we provide a mathematical characterization of the two dimensional optimal stopping problem and develop several new results. We show that allowing for interest rate uncertainty increases the optimal rotation period when the value of the optimal policy is a convex function of the current interest rate, provide plausible conditions under which this holds, and establish that increased interest rate volatility lengthens the optimal rotation period. Finally, and importantly, allowing for interest rate uncertainty as a mean reverting process and forest value as a geometric Brownian motion we provide an explicit solution for the two dimensional path-dependent optimal stopping problem. Numerical illustrations indicate that interest rate volatility has a signiﬁcant quantitative importance.
Keywords: Wicksellian rotation, stochastic interest rates, optimal stopping, free boundary problems