Stochastic Forest Management and Risk Aversion

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This paper considers the timing of timber harvesting under uncertainty. The decision of a forest manager who maximizes the expected utility is formalized using a form of the closed loop control model. The stochastic optimization problem derived is very similar to the deterministic single stand problem known as the classical Faustmann formula, but there is a notable difference. Whilst optimal rotation periods are certain in the deterministic world, they are random variables in stochastic circumstances. Stochastic optimal rotation periods are difficult to include in forest economic analyses. Fortunately, under some technical assumptions, we can find a non-stochastic variable named "barrier" which corresponds to the optimal cutting stock size in the deterministic world. This paper shows that the von Neumann-Morgenstern forest manager cuts his/her trees when the stochastic stumpage values reach a certain amount, that is the barrier. Comparative statics on the barrier were conducted to evaluate the effect of planting costs and the degree of the manager's risk aversion. The results show that the barrier rises as planting costs increase or as the Arrow-Pratt index of absolute risk aversion becomes smaller.
森林計画学会の論文