Apr 2023 -

Math-Fi seminar on 18 May

2023.05.15 Mon up
  • Date: 18 May (Thu.)
  • Place: W.W. 6th-floor, Colloquium Room and on the Web (Zoom)
  • Time: 16:30 – 18:00
  • Speaker: Toru Igarashi (Chuo University)
  • Title: Dually Flat Structure on Asset Pricing Models
  • Abstract: 
In this talk, we consider asset pricing models as dually flat manifolds and give financial interpretations to its geometric properties. We find that (1) the coefficients of dual connection correspond to the prudence of utility function; (2) a unique equilibrium is the intersection of two submanifolds (that represent investment strategies and prices); (3) the Hansen–Jagannathan distance of risk-neutral measures can be interpreted as a special case of a Bregman divergence that is a natural divergence on dually flat manifolds. We also provide a computational method for finding equilibrium numerically.

Math-Fi seminar on 27 Apr.

2023.04.24 Mon up
  • Date: 27 Apr. (Thu.)
  • Place: W.W. 6th-floor, Colloquium Room and on the Web (Zoom)
  • Time: 16:30 – 18:00
  • Speaker: Katsunori Fujie (Hokkaido University)
  • Title: Combinatorial approach to finite free probability
  • Abstract: 
Abstract: Since the 2010s, when Marcus, Spielman, and Srivastava solved the Kadison–Singer conjecture and found a connection between its solution and free probability theory, this research area has been called finite free probability.
Much progress has been made recently, and of particular interest are finite free cumulants by Octavio and Perales, where free cumulants are the basic tool used as a discretization for the characteristic function in the context of free probability.
Just recently, the speaker, Octavio Arizmendi (CIMAT) and Yuki Ueda (Hokkaido Education University) have proved a few limit theorems in finite free probability by a unified approach using finite free cumulants in arXiv:2303.01790.
The purpose of this talk is to introduce our approach.
After a brief description of the field, we will explain the combinatorial formulas that are key to the solution.
Then, as an application, we will present the limit theorems in finite free probability and their correspondence with free probability theory.
 

Math-Fi seminar on 20 Apr.

2023.04.17 Mon up
  • Date: 20 Apr. (Thu.)
  • Place: W.W. 6th-floor, Colloquium Room and on the Web (Zoom)
  • Time: 16:30 – 18:00
  • Speaker: Thomas Cavalazzi (Université de Rennes 1)
  • Title: Quantitative weak propagation of chaos for McKean-Vlasov SDEs driven by $\alpha$-stable  processes
  • Abstract: 
In this talk, we will deal with McKean-Vlasov Stochastic Differential Equations (SDEs) driven by $\alpha$-stable processes, with $\alpha \in (1,2)$. We make Hölder-type assumptions on the coefficients, with respect to both space and measure variables. 
We will study the associated semi-group, acting on functions defined on the space of probability measures, through the related backward Kolmogorov Partial Differential Equation (PDE), which describes its dynamics. 
We will focus in particular on its regularizing properties. 
The study relies on differential calculus for functions defined on the space of measures, and on Itô’s formula along flows of marginal distributions of jump processes defined with Poisson random integrals. 
We will finally use the preceding tools to prove quantitative weak propagation of chaos for the mean-field interacting particle system associated with the McKean-Vlasov SDE.

Math-Fi seminar on 6 Apr.

2023.04.04 Tue up
  • Date: 6 Apr. (Thu.)
  • Place: W.W. 6th-floor, Colloquium Room and on the Web (Zoom)
  • Time: 16:30 – 18:00
  • Speaker: Tommaso Mariotti (Scuola Normale Superiore di Pisa)
  • Title: Coding examples with Python