High frequency finance and market microstructure.
The research is devoted to the mathematical modeling and empirical characterization of financial time series at high (transaction by transaction) and ultra-high (offers to buy and sell, limit order book) frequency. The areas of interest are liquidity modeling, price formation mechanisms, and optimal order execution. Finally the group investigates possible metrics of financial market instability at high frequency and the role of market structure on the high frequency properties of prices.

Portfolio problems.
By using techniques from multivariate statistics, data mining, and the theory of complex networks, we investigate and model the dependencies between financial variables, such as stock returns, Credit Default Swap returns, and trading activity of investors or brokerage firms. The objectives are to identify and model risk factors of an asset portfolio, to build more efficient estimators of covariance matrix for optimal portfolio allocation, and to build taxonomies of investors in order to study their mutual interaction.

Systemic risk.
The group is involved in researches on the mechanisms that might lead financial markets (or the whole economy) to an excessive risk of systemic events. This is done by using mathematical and computational models and empirical analyses. The considered entities are banks or investment firms, which invest in assets and are connected through credit networks. The mechanisms investigated as possible responsible of systemic risk are excessive leverage, positive feedback loops that amplifies small perturbations, and an excessive homogeneity among portfolios.

Mean field games.
Large systems of interacting individuals are central to countless areas of science; the individuals may be people, computers, animals, or particles, and the large systems may be financial markets, networks, flocks, or fluids. People in our group have looked at the theory of mean field games (MFG) and how its study of strategic decision making in very large populations of weakly interacting individuals can be used to describe financial-related problem (e.g. models of inter-bank borrowing and lending). In addition, the MFG setting connects deeply with optimal transport theory, partial differential equations, optimization, probability and statistics with applications in machine learning problems. Collaborations on this area have been established with University of Milano, University of Torino, London School of Economics, ETH Zurich, among others.

Firm valuation.
Part of the research of the group focuses on modeling and designing methods for asset pricing and valuation theory. Using empirical analyses and valuation approaches the group investigates how misvaluation may affect the stability and efficiency of the market, by relating uncertainty and firm intrinsic value to the corresponding market prices. Together with standard stock valuation metrics, the research is devoted to incorporate the intrinsic uncertainty directly in the valuation procedure in a practitioner oriented way employing econometric modeling design.
The group collaborates with other prestigious academic institutions and industry market leaders.

Time-varying parameters models with applications to finance.
Real-world financial systems are composed by rational agents that change their behavior to adapt to shocks and news, for example financial crises, technological innovations, climate changes, pandemics. The reaction to such events, which have been observed with increasing frequency in the last years, induces then variability in the parameters of statistical/econometric models, a very challenging problem that imposes the use of dynamic models with time-varying parameters. The group is involved in such a field of research, studying both the theoretical aspects related to the problem of statistical inference of time-varying parameter models with a focus on observation driven models, such as Score-Driven models (aka Generalized Autoregressive Score models).  The main applications to finance range from Econometrics, Market Microstructure and High Frequency Data, to models of Temporal Networks and Kinetic Ising Models.

Information theory and dynamical systems in finance.
The modeling of economic and financial systems is a complex and challenging task, and, as the last financial crisis has shown, new ideas and approaches are needed to understand interlinkages and tackle instabilities. The group is involved in bringing together concepts and models based on deterministic dynamics as well as stochastic dynamics with a special emphasis on the interplay between these two aspects, both in the analysis and in the modelization of financial and economics time series.

Machine learning and artificial intelligence for finance.
The ever increasing digitalization of large amounts of data has lead to the successful adoption of Machine Learning (ML) and Artificial Intelligence (AI) techniques, based on computer algorithms that improve automatically through `experience’ (i.e. analysis of large datasets), for the study of a wide variety of statistical problems, from classification to forecasting, to name but a few. Financial data make no exception. The research is devoted to the application of such  ML and AI methods to the study of some classic and less standard problems in finance, related to volatility forecasting, portfolio optimization, time series analysis, and statistical inference.