A Real Options model for harvesting

Harvesting from natural resources, particularly fisheries, has played a central role in supporting human society, both as a source of food and economic activity. Decisions related to harvesting are influenced not only by biological and environmental conditions but also by economic incentives. Understanding how to manage these resources sustainably is essential for balancing short-term gains with long-term viability. Despite its importance, the fishing industry faces significant challenges. When fishing efforts exceed ecological limits, fish stocks can collapse due to direct human impact. In contexts where access to fishing grounds is open or poorly regulated, excessive effort can be applied simultaneously by many players, placing unsustainable pressure on the resource. To better manage this uncertainty and irreversibility of the investment, the decision to harvest can be framed as a real option. This approach treats the opportunity to fish as a right, not an obligation, allowing fishermen to delay harvesting until conditions are favourable. In this work, we formulate the optimal harvesting policy as a stochastic control problem, leading to a Hamilton-Jacobi-Bellman (HJB) partial differential equation (PDE). We solve the HJB equation numerically, allowing us to simulate and analyse optimal policies under various scenarios. The results contribute to a better understanding of sustainable exploitation and highlight the economic value of flexibility in fisheries management.