Uncertainty in economics and finance: some mathematical points of view

The goal of the project is to give some innovative mathematical contributions for a better understanding of economic and financial risk. The role of uncertainty is fundamental in the problems we will investigate, either in the sense of robustness, if no information on the probability distribution is available, or in the case of a probabilistic approach.

On one hand, we will investigate the influence of uncertainty on parameters in optimization and noncooperative game theory, with a special focus on frameworks where the decision maker has incomplete preferences. We will consider parametric models where the solution meets robustness criteria that do not require any information about the probability distribution of the parameters. Applications range from portfolio selection, where the classical mean-risk scheme can be enriched by considering additional criteria, to models of Cournot duopolistic competition, where the classical objective of profit maximization does not always provide a realistic description of the strategic behavior of the firm.

On the other hand, we will study models of stochastic optimal control and mean field games (MFG), describing Nash equilibria in complex systems, i.e. large populations of interacting rational agents. As a result, in a MFG, agents optimize over stochastic processes with known probability distributions, at the same time, the overall probability distribution evolves optimally and equilibrium conditions are satisfied. From this perspective, a special effort will be devoted to the study of stochastic differential equations. Meaningful keywords to identify the applications that we will tackle are the following: carbon emissions in electricity production, vintage capital models, inter-bank borrowing lending models with repayment, production planning problems, impact of spatial spillovers in economic models.

The impact of the expected outcomes will be twofold, both contributing to the development of the theory in the above mentioned fields and tackling innovative and up-to-date models arising in economics. We will consider problems directly arising from applications where standard mathematical techniques have to be suitably adapted and new ones have to be developed.

Elena Molho

Elisa Caprari

Benedetta Ferrario

Daria Ghilli

Hakima Bessaih (University of Florida)

Zdzislaw Brzeźniak (University of York)

Lorenzo Cerboni Baiardi (Università degli Studi di Bologna)

César Gutierrez (University of Valladolid, Spain)

Lidia Huerga Pastor (UNED, Spain)

Marta Leocata (LUISS, Roma)

Giulia Livieri (London School of Economics)

Enrico Miglierina (Università Cattolica del Sacro Cuore, Milano)