Optimal Management of Rare Earth Elements: A Stochastic Control Framework with Adaptive Investment Strategies for Sustainability

In this thesis, we will be investigating the problem of maximizing intergenerational equity in the consumption of a naturally exhaustible resource, taking into account both resource stock dynamics and environmental quality. Our model will be governed by two coupled stochastic differential equations (SDEs): one describing the evolution of the resource stock and the other the dynamics of environmental quality. Our objective will be based on optimizing consumption while balancing the trade-offs between resource depletion and environmental degradation, with an exclusive focus on fairness across generations. Specifically, our objective function will incorporate penalized consumption and social costs to reflect the need to curtail excessive consumption and mitigate environmental impacts. Through a dynamic stochastic optimization approach, this thesis explores the optimal path for resource consumption, aiming to achieve sustainability and intergenerational equity. Extensive numerical experiments validate the theoretical findings, highlighting on one hand, the crucial role of the regeneration rate of the resource and the initial stock level in determining optimal consumption strategies and, on the other hand, the necessity of adaptive investment strategies, such as dynamic investment in recycling and regeneration, to mitigate the serious issues related to resource depletion and environmental degradation ensuring therefore, sustainability across all scenarios including the less favorable ones. Finally, we will also show that by adopting the above comprehensive framework, we provide this thesis with the tools needed to contribute to the development of sustainable policies for the management of Rare Earth Elements (REEs) which are crucial for various modern technologies. The results that we obtain aim to provide a balanced approach to resource management that supports both current and future generations addressing, at the same time, the pressing issues of resource scarcity and environmental impact in a rapidly evolving global context.