News&Events

Math-Fi seminar on 6 Jan.

2022.01.06 Thu up
  • Date: 6 Jan. (Thu.)
  • Place: On the Web
  • Time: 18:00 – 19:30
  • Speaker: Xin Chen (Shanghai Jiao Tong University)
  • Title: Some results on backward stochastic differential equation on a Riemannian manifold
  • Abstract: 
In this talk, we will introduce some recent results on backward stochastic differential equation on a Riemannian manifold, including the definition of Riemannian-manifold valued BSDE, the probabilistic  representation for heat flow of harmonic map, the characterization of Navier-Stokes equation on a Riemannian manifold.
The talk is based on a joint work with Wenjie Ye.
 

Math-Fi seminar on 9 Dec.

2021.12.09 Thu up
  • Date: 9 Dec. (Thu.)
  • Place: On the Web
  • Time: 16:30 – 18:00
  • Speaker: Takwa Saidaoui (University of Tunis El Manar) 
  • Title: Behavior of some discrete hedging errors in finance; a Fourier estimator in the presence of asynchronous trading
  • Abstract: 
This thesis focuses on three topics of financial mathematics. The first part consists of a study of the L^2-norm asymptotic behavior of the error due to the replicating portfolio discretization. The averaging feature of the Asian-type payoff plays a crucial role in improving the convergence rate of the error. We show that the achieved order is explicitly related to the fractional regularity of the payoff function. The second part studies the convergence rate of the error due to the discretization of the Clark-Ocone representation for functions of Levy processes with pure jumps. The obtained rate is strongly related to the regularity index of the Sobolev space to which the payoff belongs. The last part is a study of the asymptotic behavior (central limit theorem, CLT) of the Fourier estimator of the integrated covariance under the assumption of data asynchronicity. Thus, for a determinate choice of parameters, the estimator is consistent and the CLT is valid for a sub-optimal rate.
 

Math-Fi seminar on 2 Dec.

2021.12.01 Wed up
  • Date: 2 Dec. (Thu.)
  • Place: On the Web
  • Time: 16:30 – 18:00
  • Speaker: Ngoc Khue Tran ( Pham Van Dong University) 

Math-Fi seminar on 25 Nov.

2021.11.24 Wed up
  • Date: 25 Nov. (Thu.)
  • Place: On the Web
  • Time: 16:30 – 18:00
  • Speaker:  Vlad Bally (University Paris Eiffel)
  • Title: Integration by parts and convergence in distribution norms in the CLT

Math-Fi seminar on 18 Nov.

2021.11.18 Thu up
  • Date: 18 Nov. (Thu.)
  • Place: On the Web
  • Time: 16:30 – 18:00
  • Speaker: M2 students in Kohatsu lab. (Ritsumeikan University)

Math-Fi seminar on 21 Oct.

2021.10.21 Thu up
  • Date: 21 Oct. (Thu.)
  • Place: On the Web
  • Time: 17:00 – 18:00
  • Speaker:  Yasutaka Shimizu (Waseda University)
  • Title: A quite new approach to cohort-wise mortality prediction under survival energy hypothesis
  • Abstract:
We propose a new approach to mortality prediction by “Survival Energy Model (SEM)”．We assume that a human is born with initial energy, which changes stochastically in time and the human dies when the energy vanishes. Then, the time of death is represented by the first hitting time of the survival energy (SE) process to zero.
This study assumes that SE follows a (time-inhomogeneous) diffusion process or an inverse Gaussian process, and defines the “mortality function”, which is the first hitting time distribution function of a SE process. Although SEM is a fictitious construct, we illustrate that this assumption has a high potential to yield a good parametric family of the cumulative distribution of death, and the parametric family yields surprisingly good predictions for future mortality rates. This work is published by Shimizu, et al. (2020). “Why does a human die? A structural  approach to cohort-wise mortality prediction under survival energy hypothesis”, ASTIN Bulletin, vol.51 (1), 191-219.
 

Math-Fi seminar on 14 Oct.

2021.10.13 Wed up
  • Date: 14 Oct. (Thu.)
  • Place: On the Web
  • Time: 16:30 – 18:00
  • Speaker: Tomooki Yuasa (Ritsumeikan University)
  • Title: Higher order error estimate of the discrete-time Clark–Ocone formula
  • Abstract:
In this talk, we investigate the convergence rate of the discrete-time Clark–Ocone formula provided by Akahori–Amaba–Okuma (2017).
In that paper, they mainly focus on the $L_{2}$-convergence rate of the first order error estimate related to the tracking error of the delta hedge in mathematical finance.
Here, as two extensions, we estimate “the higher order error” for Wiener functionals with an integrability index $2$ and “an arbitrary differentiability index”.

Math-Fi seminar on 26 Aug.

2021.08.26 Thu up
  • Date: 26 Aug. (Thu.)
  • Place: On the Web
  • Time: 16:30 – 18:00
  • Speaker: Yuri Imamura (Kanazawa University)
  • Title: Static Hedge via Parametrix and Symmetrization
  • Abstract:
A scheme to construct an asymptotic expansion of static hedge of barrier options for multidimensional uniform elliptic diffusions leveraging both kernel symmetrization and parametrix techniques will be introduced.
 

Math-Fi seminar on 5 Aug.

2021.08.04 Wed up
  • Date: 5 Aug. (Thu.)
  • Place: On the Web
  • Time: 16:30 – 18:00
  • Speaker: Benjamin Poignard (Osaka University)
  • Title: Estimation of High Dimensional Vector Autoregression via Sparse Precision Matrix
  • Abstract:
We consider the problem of estimating sparse structural vector autoregression (SVAR) processes via penalized precision matrix. This matrix is the output of the underlying directed acyclic graph of the SVAR process, whose zero components correspond to zero SVAR coefficients. The precision matrix estimators are deduced from the class of Bregman divergences and regularized by the SCAD, MCP and LASSO penalties. Under suitable regularity conditions, we derive error bounds for the regularized precision matrix for each Bregman divergence. Moreover, we establish the support recovery property, including the case when the penalty is non-convex. These theoretical results are supported by empirical studies.

Math-Fi seminar on 29 Jul.

2021.07.28 Wed up
  • Date: 29 Jul. (Thu.)
  • Place: On the Web
  • Time: 16:30 – 18:00
  • Speaker: Takuya Nakagawa (Ritsumeikan University)
  • Title: Projection scheme for polynomial diffusions on the unit ball
  • Abstract:
In this talk, we consider numerical schemes for polynomial diffusions on the d-dimensional unit ball, which are solutions of stochastic differential equations with a diffusion coefficient of the form (1-|x|^{2})^{1/2}. We introduce a projection scheme on the unit ball based on a backward Euler–Maruyama scheme with the projection and provide the L^{2}-rate of convergence. The main idea to consider the numerical scheme is a transformation argument introduced by Swart, J. M. (2012) for proving the pathwise uniqueness for some stochastic differential equation with a non-Lipschitz diffusion coefficient. This study is a joint work with Dai Taguchi and Tomooki Yuasa.
 

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