Faustmann optimal pine stands stochastic rotation problem

• Faustmann formula under price and wood stock uncertainties
• Application of the model to a real radiate pine cut policy
• Validation of the logistic over the Gompertz wood stock diffusion

The Faustmann optimal rotation harvesting pine stands' models under Logistic and Gompertz wood stock and Brownian price stochastic diffusion processes are reformulated as stochastic one dimensional optimal stopping problem, which are solvable with the Hamilton-Jacobi-Bellman equations. The application of these models to a Chilean forest company stands, shows discrepancies due to the absence of consideration to wood stock and price uncertainties that the company's actual cut policy shows. The stochastic models predict a significant increase of their deterministic optimal cut, with 47.0% and 48.0% in the cases of the Logistical and Gompertz wood stock diffusion respectively. The experimental data significantly validate the Faustmann stochastic logistic model giving a better approximation of the company cut policy, underestimating it by 8.09% and producing a more reliable saturation volume than the Gompertz model. The sensitivity analysis shows that both volatilities have a similar linear effect in the optimal cut, but the wood stock volatility volume elasticity of 0.687 almost double the stumpage price volume elasticity of 0.350, showing the importance of this uncertainty.