Finding equilibrium in Kyle’s model using a Neural Network

Financial markets are complex systems influenced by a variety of factors. Understanding and modeling these dynamics is crucial for predicting market behavior, managing risk, and developing trading strategies. The Kyle model, introduced by Albert Kyle in 1985, was one of the first to explore these dynamics, particularly how information is incorporated into asset prices. Despite its extensive study and widespread use in financial economics, the Kyle model relies on assumptions that limit its applicability in real-world markets. In this thesis, I aim to further explore the Kyle model by relaxing some of its key assumptions. To achieve this, I have developed a neural network that allows for a more flexible examination of market dynamics. The first chapter serves as an introduction, where I describe the financial markets, introduce the concept of market efficiency, discuss various types of securities, and outline the main market participants. The second chapter delves into the technical aspects of market efficiency, exploring how it can be unsaturated in markets. This chapter also discusses Walrasian models, market makers, and limit order books (LOB), and concludes with a discussion of empirical results related to market impact. In the third chapter, I will present Kyle’s model, beginning with the singleperiod asset case. I will then extend the model to multi-period cases, both discrete and continuous, following the original work [18]. Detailed analysis of the results and the model’s limitations will be provided. Additionally, I will discuss the Kyle model in a multi-asset context, building on the work of Mastromatteo et al. The final chapter focuses on the neural network architecture used to replicate the Kyle model in the single-period asset case. I will analyze the results obtained by relaxing certain assumptions. Finally, by making slight modifications to the network architecture, I will extend the analysis to the single-period multi-asset case.