Math-Fi seminar on 25 Mar.

2021.03.24 Wed up
  • Date: 25 Mar. (Thu.) 
  • Place: On the Web
  • Time: 16:30  – 18:00 
  • Speaker: Toshiyuki Nakayama (MUFG Bank, Ltd.)
  • Title: Convergence speed of Wong-Zakai approximation for stochastic PDEs (Joint work with Stefan Tappe)
  • Abstract: 
We talk about semi-linear stochastic differential equation (SPDE) driven by finite dimensional Brownian motion. There are a few results regarding convergence rates, such as for a second-order parabolic type (Gyöngy and Shmatkov (2006), Gyöngy and Stinga (2013)) and for the infinitesimal generator of a compact and analytic semigroup (Hausenblas(2007)).
Our goal is to establish a convergence rate without imposing restrictions on the generator, that is, the generator is allowed to be the infinitesimal generator of an arbitrary strongly continuous semigroup.
Finally, we will introduce an application example for SPDE called HJMM that appears in mathematical finance.
Today’s talk is based on a co-authored paper with Stefan Tappe “ Wong-Zakai approximations with convergence rate for stochastic partial differential equations ”, 

Math-Fi seminar on 18 Mar.

2021.03.18 Thu up
  • Date : 18 Mar. (Thu.) 
  • Place: On the Web
  • Time : 16:30 – 18:00 
  • Speaker: Noufel Frikha (Paris VII)
  • Title: On Some new integration by parts formula for finance and their Monte Carlo simulation
  • Abstract:
In this talk, I will present some new integration by parts (IBP) formulae for the marginal law at a given time maturity of killed diffusions as well as a class of stochastic volatility models with unbounded drift. Relying on a perturbation argument for Markov processes, our formulae are based on a simple Markov chain evolving on a random time grid for which we develop a tailor-made Malliavin calculus. Though such formulae could be further analyzed to study fine properties of the associated densities, our main motivation lies in their numerical approximation. Indeed, we show that an unbiased Monte Carlo path simulation method directly stems from our formulae so that it can be used in order to numerically compute with optimal complexity option prices as well as their sensitivities with respect to the initial values, the so-called Greeks, namely the Delta and Vega, for a large class of non-smooth European payoff. Numerical results are proposed to illustrate the efficiency of the method.
This talk is based on two joint works: with Arturo Kohatsu-Higa (Ritsumeikan university) and Libo Li (New South Wales university) on the one hand, with Junchao Chen (universit ́e de Paris) and Houzhi Li (universit ́e de Paris) on the other hand.

Math-Fi seminar on 12 Mar.

2021.03.12 Fri up
  • Date: 12 Mar. (Fri.)
  • Place: On the Web
  • Time: 16:30 – 18:00
  • Speakers: Ju-Yi Yen (University of Cincinatti), I-Hsun Chen (Academia Sinica), Te-Chun Wang (Academia Sinica)
  • Title: Brownian Additive Functional Averaged

Math-Fi seminar on 18 Feb.

2021.02.18 Thu up
  • Date: 18 Feb. (Thu.)
  • Place: On the Web
  • Time: 16:30  - 18:00
  • Speaker: Libo Li (University of New South Wales)
  • Title: Strong approximation of jump extended CIR and CEV processes and their mean-field extension
  • Abstract:
​In this talk, we discuss the strong approximation of jump extended CIR and CEV processes with alpha stable jumps and their mean-field extension. In particular, we discuss the Euler-Maruyama scheme, derivation of Positive Preserving schemes and finally for the mean-field extension, the propagation of chaos property and the corresponding Euler-Maruyama scheme for the particle system.

Math-Fi seminar on 21 Jan.

2021.01.21 Thu up
  • Date: 21 Jan. (Thu.) 
  • Place: On the Web 
  • Time: 16:30 – 18:00
  • Speaker: Pierre Patie (Cornell University)
  • Title: Interweaving relations
  • Abstract:
In this talk, we introduce the concept of interweaving relations as a strengthening of usual intertwining relations between Markov semigroups. We proceed by providing some  interesting applications of this new idea which includes the characterization of ergodic constants and hypercontractivity estimates for non-self-adjoint semigroups.  We illustrate these results by presenting  several examples that have emerged from the recent literature: discrete-to-continuous interacting particle models, degenerate hypoelliptic Ornstein-Uhlenbeck processes, and diffusion-to-jump  Jacobi processes.
This talk is based on joint works with L. Miclo and with P. Cheridito, A. Srapionyan and A. Vaidyanathan.

Math-Fi seminar on 14 Jan.

2021.01.14 Thu up
  • Date: 14 Jan. (Thu.)
  • Place: On the Web
  • Time: 16:30 – 18:00 
  • Speaker: Azmi Maklouf (University of Tunis El Manar)
  • Title: Error estimates for De Vylder type approximations in ruin theory
  • Abstract: 
Due to its practical use, De Vylder’s approximation of the ruin probability has been one of the most popular approximations in ruin theory and its application to insurance. Surprisingly, only heuristic and numerical evidence has supported it. Finding a mathematical estimate for its accuracy has remained an open problem, going from the original paper by De Vylder (1978) through an attempt of justification by Grandell (2000).
We carry out a mathematical and critical treatment of the problem. We more generally consider De Vylder type approximations of any order k, based on fitting the k first moments of the classical risk reserve process. Moreover, we not only deal with the ruin probability, but
also with the moments of the time of ruin, of the deficit at ruin and of the surplus before ruin.
We estimate the approximation errors in terms of the safety loading coefficient, the initial reserve and the approximation order. We show their different behaviours, and the extent to which each relative error remains small or blows up, so that one has to be careful when using this approximation. Our estimates are confirmed by numerical examples.

Math-Fi seminar on 17 Dec.

2020.12.16 Wed up
  • Date: 17 Dec. (Thu.)
  • Place: On the Web
  • Time: 16:30 – 18:00
  • Speaker: Hideitsu Hino (Institute for Statistical Mathematics) 

This seminar will be jointly organized with “Ritsumeikan University seminar on Applied Mathematics and Physics”, which is basically for Ritsumeikan University constituents. Moreover, the seminar will be presented in Japanese.

Math-Fi seminar on 10 Dec.

2020.12.10 Thu up
  • Date: 10 Dec. (Thu.)
  • Place: On the Web
  • Time: 16:30 – 18:00 
  • Speaker: Anna Aksamit (University of Sydney)
  • Title: Progressive enlargements of filtration: overview, new types, and applications
  • Abstract:
I will start with reviewing the classical results about enlargement of filtration. The main challenge is to find conditions under which martingales in the reference filtration remain semimartingales in the large filtration. If this is the case, the canonical decomposition is of particular interest. I will then present enlargement of a reference filtration through the observation of a random time and a mark. Random time considered is such that its graph is included in the countable union of graphs of stopping times. Mark revealed at this random time is assumed to satisfied generalised Jacod’s condition. Classical Jacod’s condition concerns initial enlargements and says that the conditional law of a random variable w.r.t. elements of a reference filtration is absolutely continuous w.r.t. its unconditional law. Our relaxation of Jacod’s condition accounts for the dynamic structure of the problem. Finally, I will mention some applications of progressive enlargements, in particular to optimal stopping problem.

Math-Fi seminar on 3 Dec.

2020.12.03 Thu up
  • Date: 3 Dec. (Thu.)
  • Place: On the Web
  • Time: 18:00 - 19:30 
  • Speaker: Josef Teichmann (ETH Zurich)
  • Title: Training algorithms and generalized Langevin dynamics
  • Abstract:
We investigate generalized Langevin dynamics in the sense of Baudoin-Hairer-Teichmann and its convergence to a Gibbs measure of a loss function. We derive a pathwise decay formula for entropy as in Karatzas-Schachermayer-Tschiderer and obtain in this generalized context similar results to Hu-Ren-Siska-Szpruch, which are applied to training neural networks in machine learning.
(joint work with Robert Crowell, Christa Cuchiero, Yuuki Ida and Yuri Imamura)

Math-Fi seminar on 26 Nov.

2020.11.26 Thu up
  • Date: 26 Nov. (Thu.)
  • Place: On the Web
  • Time: 16:30 – 18:00 
  • Speaker: Atsushi Takeuchi (Tokyo Woman’s Christian University)
  • Title: L\’evy processes on Riemannian manifolds