On behalf of the Scientific Committee of the "B. de Finetti Risk Seminars, Milano Lectures on the Mathematical Theory of Economics and Finance”, we are glad to invite you to participate at the following Lectures on September 24, 2025: Huyên Pham, Ecole Polytechnique (h. 16:00) and Stéphane Crépey, Université Paris Cité (h. 17:00) LOCATION The seminars will be held on September 24, 2025 starting at 16:00, Aula C20 (Via Colombo 62), Università degli Studi di Milano, Milano. TITLES AND ABSTRACTS Huyên Pham: Bridging Schrödinger and Bass for generative modeling We address the problem of generating a continuous semimartingale that interpolates prescribed initial and terminal distributions. This is formulated as an optimal transport problem that unifies the Schrödinger bridge and Bass martingale frameworks, enabling the construction of a diffusion process that simultaneously calibrates both drift and volatility to observed data. We derive an analytic characterization of the optimal diffusion’s dynamics, called Schrödinger bridge Bass (SBB) Diffusion, and show that it can be expressed as a stretched Brownian motion under an explicit change of measure. We then design a computational resolution of the SBB, offering an efficient framework for generative modeling in applications such as image synthesis and time series generation. Stéphane Crépey: Comparison of Tax and Cap-and-Trade Carbon Pricing Schemes Carbon pricing has become a central pillar of modern climate policy, with carbon taxes and emissions trading systems (ETS) serving as the two dominant approaches. Although economic theory suggests these instruments are equivalent under idealized assumptions, their performance diverges in practice due to real-world market imperfections. A particularly less explored dimension of this divergence concerns the role of financial intermediaries in emissions trading markets. This paper develops a unified framework to compare the economic and environmental performance of tax- and market-based schemes, explicitly incorporating the involvement of intermediaries. By calibrating both instruments to deliver identical emissions reductions, we assess their economic performance across alternative market structures. Our results suggests that, although the two schemes are equivalent under perfect competition, the presence of intermediaries in ETS reduces regulatory revenues and the aggregate profits of financial actors relative to carbon taxation. These effects arise from intermediaries' influence on price formation and their appropriation of part of the revenue stream. The findings underscore the importance of accounting for intermediaries' behavior in the design of carbon markets and highlight the need for further empirical research on the evolving institutional structure of emissions trading systems. Joint work with Samuel Drapeau and Mekonnen Tadese Scientific Committee Prof. Simone Cerreia-Voglio (Univ. Bocconi) Prof. Marco Frittelli (Univ. degli Studi di Milano) Prof. Fabio Maccheroni (Univ. Bocconi) Prof. Marco Maggis (Univ. degli Studi di Milano) Prof. Massimo Marinacci (Univ. Bocconi) Prof. Emanuela Rosazza Gianin (Univ. Milano-Bicocca) *** Il tuo 5x1000 al diritto allo studio Università degli Studi di Milano CF 80012650158