4 Febbraio, 2025 14:00

Four essays in energy finance

Pietro Manzoni, Politecnico di Milano

Aula Saleri - VI piano

4 Febbraio, 2025 14:00

Three essays on ESG ratings and quantitative finance

Davide Stocco, Politecnico di Milano

Aula Saleri - VI piano

3 Febbraio, 2025 11:00

Spectral analysis and exponential ergodicity of certain quantum Markov semigroups

Li Zheng, Politecnico di Milano

Aula Saleri - VI piano

31 Gennaio, 2025 11:00

Sezione di Analisi

Aggregation-diffusion equations with saturation

Alejandro Fernandez-Jimenez, University of Oxford

Aula Seminari MOX - VI piano

abstract

abstract

On this talk we will focus on the family of aggregation-diffusion equations
$$
\frac{\partial \rho}{\partial t} = \mathrm{div}\left(\mathrm{m}(\rho) \nabla (U'(\rho) + V) \right).
$$
Here, $\mathrm{m}(s)$ represents a continuous and compactly supported nonlinear mobility (saturation) not necessarily concave. $U$ corresponds to the diffusive potential and includes all the porous medium cases, i.e. $U(s) = \frac{1}{m-1} s^m$ for $m > 0$ or $U(s) = s \log (s)$ if $m = 1$. $V$ corresponds to the attractive potential and it is such that $V \geq 0$, $V \in W^{2, \infty}$.
For this problem, we discuss: Existence using a suitable regularised approximation of the problem, we prove that the problem admits an $L^1$-contractive $C_0$-semigroup; $L^1$-local minimisers of the associated free-energy functional in the corresponding class of measures; and the long-time behaviour of the constructed solutions in view of its gradient flow structure. Furthermore, we observe saturation effects leading to "freezing" behavior, i.e. free boundaries at the saturation level. Finally, we explore the properties of a corresponding implicit finite volume scheme introduced by Bailo, Carrillo and Hu.
The talk presents joint work with Prof. J.A. Carrillo and Prof. D. Gómez-Castro.

29 Gennaio, 2025 15:00

Seminari FDS

Di disfide, di righe e di compassi

Veronica Gavagna, Università di Firenze

Aula Laboratorio FDS - tiny.cc/zoomfds

abstract

abstract

Tra il 1547 e il 1548 ebbe luogo una delle più famose sfide della storia della matematica, che oppose Niccolò Tartaglia a Ludovico Ferrari. Nei Quesiti et inventioni diverse (1546) Tartaglia aveva infatti accusato Girolamo Cardano di avergli estorto anni prima la formula risolutiva dell'equazione di terzo grado e di averla poi pubblicata nella sua Ars Magna (1545); Ferrari decise quindi di confutare l'accusa rivolta al suo maestro Cardano sfidando Tartaglia nella risoluzione di trenta quesiti matematici di varia natura. A questa sfida Tartaglia rispose con altrettanti quesiti e in particolare chiese a Ferrari di dimostrare alcune proposizioni degli Elementi di Euclide senza usare il classico compasso collassabile ma il compasso fisso, il che equivale a modificare il terzo postulato. Ferrari fu in grado di raccogliere e vincere questa sfida? Scopriremo insieme come andò a finire e illustreremo possibili percorsi storico-didattici (in parte già sperimentati) per proporre, anche attraverso le fonti storiche, un approccio un po' inusuale alla geometria elementare, che induca a riflettere sul significato di dipendenza di una costruzione o di un teorema dai postulati, ovvero sulla costruzione di un sistema assiomatico-deduttivo.

28 Gennaio, 2025 11:00 oclock

Sezione di Geometria, Algebra e loro applicazioni

Generalized word problem of bounded automata groups

Davide Perego, Université di Genève

Aula Seminari - III Piano

abstract

abstract

The membership subgroup problem asks whether an element in a group belongs to a fixed subgroup. This gives rise to a formal language and, in the case of stabilizers, to a graph-theoretic interpretation. After defining groups described by automata, we will study the membership languages for stabilizers in this class. In particular, we will make use of Lindenmayer's systems, which were originally introduced in biology, but recently have successfully been exploited in combinatorial group theory.

28 Gennaio, 2025 10:00

Laboratorio FDS

The 4 dimensions of a Linear Algebra course

Ana Moura Santos, Instituto Superiore Tecnico - University of Lisbon

Aula Laboratorio FDS e online tiny.cc/zoomfds

abstract

abstract

Based on my experience of more than 20 years teaching Linear Algebra, and the insight I have gained into learning methodologies in an engineering school, I would like to share experiences and ideas on the 4 dimensions to achieve good results in a Linear Algebra course: the course syllabus, the textbook(s) and MOOCs, student-centered active learning , and formative assessment. 

27 Gennaio, 2025 16:00

Sezione di Finanza Quantitativa

Market Making with fads, Informed and Uninformed traders

Adrien Mathieu, Oxford University

Aula seminari, 3° piano.

abstract

abstract

We characterize the solutions to a continuous-time optimal liquidity provision problem in a market populated by informed and uninformed traders. In our model, the asset price exhibits fads — these are short-term deviations from the fundamental value of the asset. Conditional on the value of the fad, we model how informed traders and uninformed traders arrive in the market. The market maker knows of the two groups of traders but only observes the anonymous order arrivals. We study both the complete information and the partial information versions of the control problem faced by the market maker. In such frameworks, we characterize the value of information, and we find the price of liquidity as a function of the proportion of informed traders in the market. Lastly, for the partial information setup, we explore how to go beyond the Kalman-Bucy filter to extract information about the fad from the market arrivals.

24 Gennaio, 2025 14:30

Sezione di Finanza Quantitativa

Tail calibration of probabilistic forecasts

Johanna Ziegel, ETH Zurich

B.5.1

abstract

abstract

Probabilistic forecasts comprehensively describe the uncertainty in the unknown future outcome, making them essential for decision making and risk management. While several methods have been introduced to evaluate probabilistic forecasts, existing evaluation techniques are ill-suited to the evaluation of tail properties of such forecasts. However, these tail properties are often of particular interest to forecast users due to the severe impacts caused by extreme outcomes. In this work, we introduce a general notion of tail calibration for probabilistic forecasts, which allows forecasters to assess the reliability of their predictions for extreme outcomes. We study the relationships between tail calibration and standard notions of forecast calibration, and discuss connections to peaks-overthreshold models in extreme value theory. Diagnostic tools are introduced and applied in a case study on European precipitation forecasts.
Joint work with Sam Allen, Jonathan Koh, Johan Segers.

Johanna Ziegel is Professor of Statistics at ETH Zurich, Switzerland, since 2024. She is Visiting Scientist at the Heidelberg Institute for Theoretical Studies, Germany. Johanna obtained her PhD in 2009 at ETH Zurich and then held postdoctoral in Melbourne, Australia, and Heidelberg, Germany. In 2012 she joined the University of Bern, where she was promoted to Associate Professor in 2018 and to Full Professor in 2023. She has been a Council Member of the Bernoulli Society and has served as Associate Editor for several leading international journals including Mathematical Finance, Bernoulli, JASA: Theory & Methods, Journal of Financial Econometrics, and International Journal of Forecasting. She won the Credit Swiss Award for Best Teaching at the University of Bern in 2022.

23 Gennaio, 2025 14:00

MOX Colloquia

A quasi-optimal space-time finite element method for parabolic equations

Rob Stevenson, University of Amsterdam

B.5.3, V Piano, Edificio 14 (Nave), Politecnico di Milano

abstract

abstract

We outline the (potential) advantages of simultaneous space-time discretisations of parabolic evolution equations, and illustrate them with some numerical results. Other than for elliptic equations there is not one obvious variational formulation, and we present several possibilities. They have in common that the bilinear form is not coercive so that one has to resort to minimal residual discretisations, in most cases in a dual norm which leads to a saddle point problem. We present some technical details concerning adaptive mesh refinement, the construction of uniformly bounded Fortin interpolators, and optimal preconditioning.

Contatto:
marco.verani@polimi.it

Rob Stevenson is professor of Applied Analysis at the University of Amsterdam, The Netherlands. In 1990 he received his PhD from the University of Utrecht. He held positions at the University of Utrecht, the Eindhoven University of Technology, and the Radboud University Nijmegen. He was appointed professor at the University of Amsterdam in 2007. He has served/is serving in the editorial boards of several journals in Numerical Analysis and Computational Mathematics. His research is concerned with the numerical solution of partial differential equations. The main focus of his research is on finite element and wavelet methods, multi-level solvers, least squares discretizations, adaptive methods, and space-time methods.