GEOMETRY OF MULTI-AGENTS SIMULATION

Understanding the dynamics of stock market, has always been a goal for researchers, because investors need accurate tools to conduct their investments. In this thesis, the stock market will be modeled with a multi-agent reinforcement learning environment. Once trained this model will allow to collect data accurately and to know everything about transactions, the financial status of investors and macroeconomic variables such as price of shares. These data will be analyzed using topological data analysis (TDA), which will allow to observe the shape of the underlying structure hidden in data. Extensive use was made of persistent entropy, in order to have a quantitative measure of financial status of investors in an instant of time. Then, thanks to the sliding window, it was possible to extrapolate a signal that represents the dynamics of the stock market over time. We will therefore calculate the Pearson correlation between the entropy signal in homology 1 and the momentum of the price obtaining a positive correlation value.