Does Risk Aversion Accelerate Optimal Forest Rotation under Uncertainty?
We use a Wicksellian single rotation framework to analyze the impact of the intertemporally fluctuating and stochastic mean-reverting interest rate process on the optimal harvesting threshold and thereby the expected length of the rotation period, when forest value is also stochastic following geometric Brownian motion and landowners are risk-averse. We provide an explicit solution for the two-dimensional path-dependent rotation problem and demonstrate that higher interest rate volatility increases, while higher risk aversion decreases the optimal harvesting threshold. Moreover, under risk aversion increased forest value volatility decreases the optimal harvesting threshold, while it has no effect under risk neutrality. Numerical illustrations indicate that higher interest rate volatility will raise the expected rotation period at an increasing rate, while higher forest value volatility will decrease its sensitivity under risk aversion.
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