Research areas in Mathematics and Statistics
The scientific production of the Pavia research group in Mathematics for Economics and Finance is divided into four main directions, combining theoretical rigor with practical applications:
- Quantitative Finance: Driven by the development of advanced models for derivative pricing, static and dynamic portfolio optimization, and financial market microstructure, this line of research integrates machine learning, deep learning, network analysis, fuzzy logic, and methods from financial econometrics.
- Theory of Stochastic Processes: Focuses on advanced stochastic analysis in infinite-dimensional spaces, with an emphasis on stochastic partial differential equations. It investigates the existence and uniqueness of solutions for complex systems perturbed by noise and studies their invariant measures to describe their asymptotic behavior.
- Decision Theory and Optimization: A historical strand of research investigating vector optimization, multicriteria choices, and preference models under conditions of uncertainty, providing the mathematical framework to understand the rationality and behavior of economic agents.
- Optimal Control and Mean Field Games: Cutting-edge research using advanced mathematical models to analyze complex macroeconomic systems with numerous interacting agents. By way of example, the research examines the spatio-temporal evolution of economic activities and human capital dynamics, with spatial interactions, as well as quantitative multi-agent models for the study of climate change.
The research outputs have appeared in international journals such as Economic Theory, ESAIM: Control, Optimisation and Calculus of Variations, European Journal of Operational Research, Insurance: Mathematics and Economics, Journal of Banking and Finance, Journal of Business & Economic Statistics, Journal of Econometrics, Journal of Economic Dynamics and Control, Journal of Global Optimization, Journal of Mathematical Economics, Journal of Optimization Theory and Applications, Management Science, Operations Research, Quantitative Finance, SIAM Journal on Mathematical Analysis, SIAM Journal on Optimization, Stochastic Processes and their Applications, Theory of Probability & its Applications.
The researchers of the group are:
Michele Ricciardi (post-doc)
The research of the Statistics group promotes the production of scientific knowledge, advanced training, and applied research in the field of data analysis, statistical inference, machine learning, and their applications. The main lines of research include graphical and network models, the measurement of financial risks and financial technologies (fintech), the evaluation of the quality and security of the applications of artificial intelligence and quantum computing, the measurement of environmental, social, and governance sustainability.
The results of the the, research have appeared in international scientific journals, including Journal of the Royal Statistical Society (A, B, C), Journal of Business and Economic Statistics, Biometrika, Statistics in Medicine, International Journal of Forecasting, Expert Systems with applications, Neurocomputing, Artificial Intelligence Review, Mathematical models and methods in applied sciences, Annals of operations research, Journal of the Operations research society, Physica A: statistical mechanics and its applications, Finance research letters.
The researchers of the group are:
As well as the post-doc researchers:
Golnoosh Babaei
Costanza Bosone
Barbara Tarantino
Rasha Zieni