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This paper demonstrates the capabilities of Deep Reinforcement Learning algorithms

in the area of financial portfolio management. This field has seen a huge development in recent years, because of the increased computational power and increased research in sequential decision making through control theory.

In this paper we have designed an environment for trading that is compatible with OpenAI gym framework. It simulates real market behavior and can be utilized to assess different portfolio optimization strategies. Also it is used to train reinforcement learning algorithms (DDPG & DQN). The agents can act in this environment by allocating the weights of stocks in the portfolio in each time step.

We have implemented Deep Reinforcement Learning models that act as autonomous portfolio optimization agents. In particular, we focus on Deep Deterministic Policy Gradient

and Deep Q-Network algorithms, which are model-free reinforcement learning algorithms that learn the quality of actions and tell agents what action to take under what circumstances.

We have performed a comparative analysis of the Reinforcement Learning based optimization strategy and more traditional «Follow the Winner», «Follow the Loser», «Random» and «Uniformly Balanced» strategies to find out which agent outperforms all the other strategies.

Table of Contents

List ob abbreviations.....................................................................................................5 Notation.........................................................................................................................6 Introduction...................................................................................................................7 Part 1. Theoretical Part. (Background)........................................................................10 Chapter 1. Deep Learning............................................................................................10

1.1 Perceptron..........................................................................................................10 1.2 Neural Network.................................................................................................11 1.3 Activation Function...........................................................................................12 1.4 Loss Function....................................................................................................14 1.5 Backpropagation................................................................................................16 1.6 Optimization Algorithms...................................................................................16 1.7 Gradient Descent Optimization Algorithms......................................................16 1.8 Overfitting.........................................................................................................21

Chapter 2. Reinforcement Learning............................................................................22 2.1 Key Concepts.....................................................................................................22 2.2 Taxonomy of RL Algorithms.............................................................................30

Chapter 3. Deep Reinforcement Learning...................................................................33 3.1 Vanilla Policy Gradient (VPG)..........................................................................33 3.2 Deep Deterministic Policy Gradient (DDPG)...................................................35

Chapter 4. Financial Theory........................................................................................40 4.1 Financial Terms and Concepts...........................................................................40 4.2 Statistical Moments...........................................................................................42

Part 2. Practical Part....................................................................................................49 Chapter 5. Trading environment..................................................................................49

5.1 OpenAI Gym.....................................................................................................49 5.2 MDP model........................................................................................................49 5.3 Action Space......................................................................................................50 5.4 State and Observation Space.............................................................................50 5.5 Reward signal....................................................................................................50 5.6 Trading environment implementation...............................................................51 5.7 Dataset...............................................................................................................51

Chapter 6. Trading Agents...........................................................................................52 6.1 Base Agent.........................................................................................................52 6.2 Regular Agents..................................................................................................52 6.3 DQN Agent........................................................................................................53 6.4 DDPG Agent......................................................................................................53

Chapter 7. Experiments...............................................................................................55 7.1 Experiments in OpenAI Gym environment.......................................................55 7.2 Experiments in Trading Environment...............................................................56

Results.....................................................................................................................59 Conclusions.............................................................................................................61 References...............................................................................................................62

Application 1. Trading environment package listing...................................................64 Application 2. DDPG Agent package listing...............................................................70 Application 3. Financial metrics package listing.........................................................76

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