Wicksellian theory of forest rotation under interest rate variability

We apply the Wicksellian single rotation framework to cover the unexplored case of variable and stochastic interest rate. We provide a mathematical characterization of the two-dimensional optimal stopping problem and show in the presence of amenity valuation that increased interest-rate volatility lengthens the optimal rotation period and increases the value of the optimal policy. By modelling the interest rate as a mean reverting process and forest value as a geometric Brownian motion and abstracting from amenity valuation, we present an explicit solution for the problem. Numerical illustrations indicate that interest-rate volatility has a significant and non-linear impact on optimal rotation.