Buongiorno, vi segnaliamo le date e i contenuti del secondo ciclo di seminari estivi online sulle applicazioni della probabilità in economia organizzate dal gruppo UMI PRISMA. 16 luglio 2026, ore 14 Daria Ghilli, Department of Economics and Management, University of Pavia Title: Mean Field Games in infinite dimensional spaces and applications to economics Abstract: We present an overview of mean field game models for large populations of forward-looking agents whose individual state is naturally infinite-dimensional. This situation arises when agents’ dynamics involve variables such as age, spatial position, memory or path-dependent effects, or delay. These features are common in economic applications, including vintage capital models, production planning problems, and systemic risk. We explain how infinite-dimensional techniques make it possible to reformulate such dynamics as abstract evolution equations in Hilbert spaces, often eliminating the explicit delay by enlarging the state variable. We then present some recent results and discuss applications to vintage capital models and systemic risk. 23 luglio 2026, ore 14 Miguel Angel Sordo Diaz, Departamento de Estadística e Investigación Operativa, Universidad de Cádiz Title: A Spearman-like coefficient for upper-tail association analysis Abstract: Quantifying association during extreme events is of paramount importance in fields such as finance, insurance, and environmental sciences. Classical correlation measures often fail to capture co-movements in the tails of distributions, while traditional boundary tail coefficients collapse under asymptotic independence, rendering them blind to subasymptotic concentration. In this paper, we introduce a unified framework of Spearman-like, tail-sensitive indices constructed via the ranks and concomitants of the data to assess localized association conditional on large threshold exceedances. We establish two complementary families of measures: a discrete two-parameter family that encompasses Spearman's $\rho$ as a special case, and a continuous single-parameter family obtained as its asymptotic limit. This threshold-defined framework offers a flexible, interpretable diagnostic tool that continuously tracks tail-association paths and successfully discriminates among fundamentally distinct subasymptotic structures where classical boundary indicators vanish. For both families, we investigate their theoretical properties - including their limiting behavior at the absolute boundary - propose empirical plug-in estimators, and derive their asymptotic distributions. The operational advantages of the indices are verified through analytical illustrations across diverse copula families and demonstrated via an empirical application to global catastrophic risk. 25 settembre 2026 ore 14 Sara Biagini, Department of AI, Data and Decision Sciences, LUISS University, Rome Title: An introduction to carbon markets regulation: carbon neutrality and Net-Zero Abstract: After introducing carbon markets, we analyze the impact of carbon dioxide regulation on a system of polluting, heterogeneous companies. We consider two compliance frameworks: one based on an emission trading system (ETS) mechanism and the other relying only on abatement efforts. The shocks in the economy are spanned by a multivariate Brownian motion, and the companies’ emissions are modeled as general diffusions. Firms must match their projected emission imbalance with their reduction effort at the compliance date in both frameworks. Under the ETS program, to do so firms can both abate and trade carbon permits in the ETS permits exchange. Existence and uniqueness of the optimal abatement and trade, together with the equilibrium carbon price, are proven under mild necessary and sufficient conditions. The optimizers and the carbon price are explicit, and their analytic expressions provide an instance of classic economic principles. Numerical examples illustrate the flexibility of the model in the study of the effect of significant allocation policies. Under the net-zero framework, firms can only rely on abatement, which is also provided in closed-form. Seguiranno, per ciascun seminario, le istruzioni per partecipare. Cordiali saluti dagli organizzatori: Giulio Bottazzi, Alessandro Calvia, Marco Capaldo, Enrico Scalas