Financial and actuarial mathematics concerns with the mathematical formulation and analysis of financial and actuarial questions, and in the last decades it has become an important research direction both in academics and in the industry.
Our research uses sound mathematical approaches in order to tackle relevant problems arising in financial and commodity markets, as well as in actuarial science. Most of the techniques that we employ are drawn from probability theory and stochastic analysis, the theory of partial differential equations, and stochastic control. The latter allows to tackle optimal agents' dynamic choices in stochastic environements, and we are particularly interested in problems of singular stochastic control, optimal stopping and their related free-boundary analysis. These problems find natural applications in questions of optimal irreversible/partially reversible investment, optimal harvesting and dividend distribution, optimal consumption with intertemporal substitution, and optimal management of macroeconomic quantities like public debt or interest rates.
Combining control theoretic techniques with game theory, we also investigate stochastic games modeling situations where multiple agents compete or cooperate to achieve certain goals. This is the case of capacity expansion games in an oligopoly, of strategic contribution in a public good, or of real option games. We consider N-player games as well as mean-field games, with the aim of showing existence of equilibria, providing their characterization, and deriving possible approximating algorithm leading to a numerical implementation.