Probability & Statistics Seminar

Upcoming sessions :

• Thursday 10.10.2024, 13h, MNO 1.020
  Charles-Philippe Manuel Diez (Université du Luxembourg), Introduction to free probability
  Abstract: In this talk we will introduce the concept of “free probability”, a theory developed by Voiculescu in the early 80s. We will introduce the notion of a non-commutative probability space with some examples, and the glossary between classical and free probability. We will then introduce the notion of “freeness”, which is the free analogue of classical (tensor) independence, and which was the initial motivation for Voiculescu to understand the structure of special von Neumann algebras called free group factors. We will then explore the analytical aspect of Voiculescu and the combinatorial structure of free probability via the lattice non-crossing partitions discovered by Speicher. We will also present a deep and surprising connection to random matrix theory discovered by Voiculescu in 1991. This latter result was of profound importance in proving breakthrough results in the world of operator algebras, but also in the development of random matrix theory. Finally, if time permits, we will present some of these important results in a heuristic way by introducing the mathematical microstates approach to free entropy.

• Thursday 17.10.2024, 13h, MNO 1.010
  Grégoire Valentin Michel Szymanski (Université du Luxembourg), Statistical inference for rough volatility
  Abstract: Rough volatility models have emerged as a powerful framework to capture the intricate dynamics and irregularities of financial markets. These models, characterized by fractional Brownian motion (fBM) with a Hurst parameter H < 1/2, provide an effective description of the high-frequency, rough behavior of stochastic volatility. In this presentation, we offer a comprehensive overview of three distinct contributions that tackle various facets of the challenging problem of estimating the Hurst parameter H. In this talk, we review the methodology proposed in Volatility is Rough to quantify the roughness of the volatility process. We discuss its implications from a financial perspective and address the statistical limitations inherent to this approach. We focus on the estimation of H from discrete price observations within a semi-parametric setting, without assuming any predefined relationship between volatility estimators and true volatility. Our approach achieves the optimal minimax rate of convergence for parametric rough volatility models. Specifically, we show that the convergence rate for estimating H can reach n^{-1/(4H+2)} for small values of H.

• Thursday 24.10.2024, 13h30, MNO 1.010
  Lorenzo Cristofaro (Université du Luxembourg), A Class of non-Gaussian Measures and Related Analysis
  Abstract: During the last decades infinite-dimensional analysis has been developed through the use of non-Gaussian analysis. Indeed, the tools of White Noise Analysis have been generalized for non-Gaussian measures to obtain notions and characterizations similar to Gaussian Analysis. In this talk, we present new results about the use of generalized Wright functions as characteristic functional, the cases of the associated non-Gaussian measures and their properties.

• Monday 18.11.2024, 13h, MNO 1.040
  Jose Ameijeiras-Alonso (Universidade de Santiago de Compostela), TBA
  Abstract:TBA

• Thursday 21.11.2024, 13h30, MNO 1.010
  Sven Wang (Humboldt-Universität zu Berlin), TBA
  Abstract:TBA

• Thursday 28.11.2024, 13h30, MNO 1.010
  Hermine Biermé (Université de Tours), TBA
  Abstract:TBA

• Thursday 5.12.2024, 13h30, MNO 1.010
  Alba García-Ruiz (Universidad Autónoma de Madrid, ICMAT), TBA
  Abstract:TBA

Past sessions :