Sustainable resource management through stochastic optimal control: A framework for balancing present and future consumption of exhaustible resources

The availability of natural resources depends on their nature. Renewable ones are accessible to both current and future generations, unlike non-renewable ones. Oil, coal and natural gas are an example of these exhaustible resources, with limited availability on our planet. When these resources are consumed, their availability decreases, causing poverty, inequality, and conflict. Thus, policymakers, in particu lar at the supranational level, have the task of promoting sustainable consumption practices that ensure equity between generations. To ensure well-being between gen erations and long-term sustainability of these resources, overconsumption of them must be penalized. With these premises, the decision maker must solve the problem of maximizing intergenerational utility. It requires the introduction of a variable t representing the generations, the definition of a utility function associated with the consumption of resources at time t and, finally, the maximization of the ag gregate utility functions of the different generations, where consumption represents the variable of problem control. In this thesis, the conventional approach of “time preference” is rejected, introducing a discount factor that is independent of time, but which penalizes overconsumption. This approach encourages a more equitable distri bution of resources, ensuring that current generations do not consume at the expense of future ones. We formulated a stochastic optimal control problem to address this issue. The model takes into account uncertainty in availability and regeneration of the resource, making it applicable to real-world scenarios. This model is a nonlinear optimization model that can be solved using the Dynamic Programming Principle. In this thesis, we consider the problem over a finite time horizon to avoid the limi tations associated with the infinite case. Indeed, the infinite approach often leads to extreme results, like the so-called “golden rule”, which imposes a minimal current consumption to preserve resources for future generations. After developing the theoretical model, we ran numerical simulations to examine how the system behaves in various scenarios. We studied how much different parameters influence the sustainable use of limited resources through a sensitivity analysis of the model. The results reveal that the optimal consumption strategy for an exhaustible resource strongly depends on two key factors, the resource’s regeneration rate and the initial available stock.