We provide a data-driven approach to regime  classification. Regimes are identified with distributions of path signatures; a distance between these distributions is described and a data-driven clustering algorithm is applied to propose natural classifications of market regimes with as little manual specification as possible.

The Signature transform can be used as a feature extraction method for time-sequential data. In practice, a key problem for this method is to decide its truncated order. We will give a brief introduction for Signature and discuss how truncated order can be increased as a function of the observation size under linear functionalSignature regression framework.

Distributional Reinforcement learning is one of the most promising advances to deep Q reinforcement learning in recent years. We show that by adapting it to the trading environment we can outperform the previous cutting-edge reinforcement learning tools for optimal execution, in environments using both simulated and historical data.

Rough volatility models are able to capture and explain stylised facts observed from historical market data in volatility time series and in the implied volatility of option prices. Since the fits to implied volatility surfaces are promising, rough volatility models open the door to further calibration problems, including the challenging issue of joint calibration of S&P 500 and VIX implied volatility surfaces.

This last decade, markets have become more automatized and trading frequency has made calibration of models, such as the SABR model, more time-consuming. This time constraint is critical and will become more pronounced in the future. Neural Networks offer the possibility to offline the calibration and to obtain updated parameters instantaneously.

Machine learning models are developed to predict which start-up companies are successful investment opportunities for Venture Capital investors, with models trained on a time series database of start-up company snapshots. We show that this approach increases the investment success rate by at least 50% when compared with the success rate of the average Venture Capital investor.