This thesis investigates the index tracking problem through a novel approach based on the principles of dynamic programming, with a focus on modern deep- reinforcement learning techniques. Given the increasing popularity of passively managed funds like exchange-traded funds, finding innovative ways to replicate a selected financial index efficiently is a significant challenge in today’s computational finance. This approach comes with its own set of difficulties, primarily related to data requirements, as the method’s great flexibility comes at the cost of significant computational time and the large volume of data necessary for training. Never- theless, building such a model allows for the use of a highly realistic transaction cost model that is even capable to incorporate taxation: this makes the model also suitable for private investors, who are usually the most affected by the model simplifications typically found in the literature.