Optimal risk management problem of natural resources: Application to oil drilling

The aim of this paper is to determine the optimal balance between extraction and storage of a natural resource (in particular crude oil) over time under a large array of environmental, operational and financial constraints for an infinite maturity time. We consider a manager that owns an oil field from which he can extract oil and decides to sell or store it. This operational strategy has to be carried out in continuous time and has to satisfy physical, operational, environmental and financial constraints such as storage capacity, crude oil spot price volatility, amount available for possible extraction or maximum amount that could be invested at time t for the extraction choice. The costs of storage and extraction are also taken into account to better fit the real market scenario. We solve the optimization problem of the manager's profit under this large array of constraints and provide an optimal strategy. We then examine different numerical scenarios to check the robustness and the corresponding optimal strategies given by our model, which is obtained by a numerical approach, with respect to different possible events related to the market , environmental policies or ecological constraints