Seminars

Math-Fi seminar on 18 Jun.

2020.06.18 Thu up
  • Date: 18 Jun.  (Thu.)
  • Place: On the Web
  • Time: 16:00-17:00
  • Speaker: Arturo Kohatsu-Higa (Ritsumeikan) 
  • Title: 信頼空間、Light TailかFat Tailか？
 

Math-Fi seminar on 4 Jun.

2020.06.04 Thu up
  • Date: 4 Jun.  (Thu.)
  • Place: On the Web
  • Time: 16:30-18:00
  • Speaker: Guanting Liu (UNSW)
  • Title: A positivity-preserving numerical scheme for the alpha-CEV process
  • Abstract: 
​We propose and prove strong convergence of a positivity-preserving implicit numerical scheme for jump-extended Cox-Ingersoll-Ross (CIR) process and Constant-Elasticity-of-Variance (CEV) process, where the jumps are governed by a compensated spectrally positive alpha-stable Levy process for alpha in (1, 2).
This class of models have first been studied in the context of continuous branching processes with interaction and/or immigration, and in this class a model has been introduced to mathematical finance for modelling sovereign interest rates and the energy market, which was named the alpha-CIR process. Numerical schemes for jump-extended CIR and CEV processes in the current literature, to the best of our knowledge, have all focused on the case of finite activity jumps (e.g. Poisson jumps) except our previous work studying a positivity-preserving scheme for the alpha-CIR process. In this paper, besides strong convergence we also obtain bounded beta-moments of the numerical scheme, for beta in [1, alpha), which allows us to left the boundedness requirement on the jump coefficient, and hence avoid truncation.
 

Math-Fi seminar on 28 May

2020.05.28 Thu up
Date: 28 May (Thu.)
Place: On the Web
Time: 16:30-18:00
Speaker: Takafumi Amaba (Fukuoka University)
Title: Bayesian CNNとTsirelson-Vershikによる黒色雑音の構成について
 

Math-Fi seminar on 7 May

2020.05.07 Thu up
  • Date: 7 May (Thu.)
  • Place: On the Web
  • Time: 16:30-18:00
  • Speaker: Takuya Nakagawa (Ritsumeikan University)
  • Title: On a Monte Carlo scheme for a stochasticquantity of SPDEs with discontinuous initial conditions
  • Abstract:
The aim of this seminar is to study the simulation of an expectation of a stochastic quantity $\e[f(u(t,x))]$ for a solution of stochastic partial differential equation driven by multiplicative noise with a non-smooth coefficients and a boundary condition: $Lu(t,x)=h(t,x) \dot{W}(t,x)$.
We first define a Monte Carlo scheme $P_{t}^{(N,M,L)}f(x)$ for $P_{t}f(x):=\e[f(u(t,x))]$, where $f$ is a bounded measurable function $f$ and $u(t,x)$ is a solution of stochastic partial differential equation given by Duhamel’s formula, and then we prove the convergence of the Monte Carlo scheme $P_{t}^{(N,M,L)}f(x)$ to $P_{t}f(x)$ and  the rate of weak error.
In addition, we introduce results of numerical experiments about the convergence error and the Central limit theorem for the scheme.

Math-Fi seminar on 23 Apr.

2020.04.23 Thu up
  • Date:  23 Apr. (Thu.)
  • Place: On the Web
  • Time: 16:30-18:00
  • Speaker: Dai Taguchi (Okayama University)
  • Title: Multi-dimensional Avikainen’s estimates
  • Abstract:
Avikainen provided a sharp upper bound of the expectation of |f(X)-f(Y)|^{q} by the expectation of |X-Y|^{p}, for any one-dimensional random variables X with bounded density and Y, and function of bounded variation f. In this talk, we consider multi-dimensional analogues of this estimate for any function of bounded variation in R^{d}, Orlicz–Sobolev spaces, Sobolev spaces with variable exponents or fractional Sobolev spaces.

We apply main statements to the numerical analysis on irregular functional of a solution to stochastic differential equations based on the Euler–Maruyama scheme and the multilevel Monte Carlo method, and L^{2}-time regularity of decoupled forward–backward stochastic differential equations with irregular terminal conditions.

This is joint work with Akihiro Tanaka (Osaka university) and Tomooki Yuasa (Ritsumeikan University).

Math-Fi seminar on 9 Apr.

2020.04.09 Thu up
  • Date: 9 Apr. (Thu.)
  • Place: On the Web
  • Time: 16:30-18:00
  • Speaker: Pierre Bras (École normale supérieure Paris)
  • Title: Acceleration of stochastic optimization algorithms
  • abstract: 
I will introduce stochastic algorithms to solve optimization problems, arising in machine learning or mathematical finance. Then, starting with the basic stochastic gradient algorithm, we will see how one can modify it so that to accelerate the convergence towards the optimal solution.
 

Math-Fi seminar on 26 Mar.

2020.04.09 Thu up
  • Date: 26 Mar. (Thu.)
  • Place: On the Web
  • Time: 16:30-18:00
  • Speaker: Shin Harase (Ritsumeikan University)
  • Title: マルコフ連鎖モンテカルロ（MCMC）法の準モンテカルロ法化

Math-Fi seminar on 27 Feb.

2020.02.07 Fri up
  • Date: 27 Feb. (Thu.)
  • Place: W.W. 6th-floor, Colloquium Room
  • Time: 16:30-18:00
  • Speaker: Pierre Bras (École normale supérieure Paris)
  • Title: Bayesian inference and Metropolis-Hastings algorithms (provisional title)
  • Abstract:
​Markov chains Monte Carlo (MCMC) methods are simulation methods for sampling from a probability distribution from which direct sampling is difficult, and are particulary used in bayesian learning. The Metropolis-Hastings algorithm is one of the most popular. I will present the algorithm, then prove convergence results, and present the adaptation of the algorithm to stochastic optimization problems. Please come and join us.
 

Math-Fi seminar on 13 Feb.

2020.02.07 Fri up
  • Date: 13 Feb. (Thu.)
  • Place: W.W. 6th-floor, Colloquium Room
  • Time: 16:30-18:00
  • Speaker: Pierre Bras (École normale supérieure Paris)
  • Title: Stochastic optimization and neural networks
  • Abstract: 
Stochastic algorithms aim to solve optimization problems by randomly exploring the state space. They appear in machine learning and in financial mathematics, and are the main tool used for calibrating neural networks. I will demonstrate some convergence properties, and present the gradient descent in the framework of neural networks.
 

Math-Fi seminar on 17 Jan.

2020.01.14 Tue up
  • Date: 17 Jan. (Fri.)
  • Place: W.W. 6th-floor, Colloquium Room
  • Time: 16:30-18:40


  • First Speaker: Yushi Hamaguchi (Kyoto University)
  • Time: 16:30-17:30
  • Title: Time-inconsistent consumption-investment problems in incomplete markets
 
  • Second Speaker: Yuki Ueda (Hokkaido University) 
  • Time: 17:40-18:40
  • Title: Introduction to free probability theory and infinitely divisible distributions

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