Portfolio management is the task of constantly redistributing the wealth of an investor into different financial products known as assets in order to maximize the overall profit during the trading period while maintaining an acceptable level of risk. Traditionally, this problem has been heavily studied using a static approach, leading to the creation of what is known as the Modern Portfolio Theory by economist H. Markowitz in 1952. However, more recent developments in the field of optimization of dynamical systems, especially via reinforcement learning, have sparked a growing interest in applying these new techniques to the portfolio optimization task. In this thesis, we represent the trading environment as a discrete-time stochastic dynamical system and apply deep learning based reinforcement learning algorithms to train an agent to learn a trading strategy that optimizes a given objective.