The Option Value of Harvesting a Renewable Resource

We analyze multi-period harvest problems for a renewable resource under biological uncertainty when harvesting is size-dependant. First, we show that the decision to harvest can be modeled as a real option and we derive analytical expressions for the value of the resource stock and the mean time between harvests, with and without uncertainty. We then illustrate numerically how uncertainty affects the decision to harvest: when uncertainty increases from zero, the amount harvested and the stock biomass at harvest first increase, and then decrease because of the risk of extinction when uncertainty is high enough. This paper is a first step towards defining sustainable harvesting rules under uncertainty.