Department of Mathematical Sciences, Ritsumeikan University Web Page

Math-Finance seminar

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

Math-Fi seminar on 9 Jan.

2020.01.07 Tue up

Date: 9 Jan. (Thu.)
Place: W.W. 6th-floor, Colloquium Room
Time: 16:00-19:00

First Speaker: Katsushi Nakajima (Ritsumeikan Asia Pacific University)
Time: 16:00-17:30
Title: TBA

Second Speaker: Koya Sakakibara (Kyoto University)
Time: 17:30-19:00
Title: Numerical analysis of interface problem
Abstract:

The interface appears in several problems, such as fluid dynamics between two different liquids. To study its evolution and dynamics forms the basis of the research in natural science. Although there are several mathematical studies for interfacial phenomena, they are, in general, so difficult, and numerical study becomes an essential tool in this field.

In this talk, I will talk about the numerical analysis of interface problem, and especially consider two issues: The Hele-Shaw problem and grain boundary. The Hele-Shaw problem describes the motion of viscous fluid in a quasi-two-dimensional space, which started from a short paper by Henry Selby Hele-Shaw (1854–1941). It is now recognized as a basic mathematical model to study the fingering phenomena (also known as the Saffman–Taylor instability), and several researchers have studied this problem; however, there are still several open questions. A problem on the grain boundary appears in the field of material science. A grain boundary is an interface between two grains, or crystallites, in a polycrystalline material. It is the two-dimensional defect in the crystal structure. The study of grain boundaries and their effects on the mechanical, electrical, and other properties of materials forms an essential topic in material science. My study aims to understand the mechanism of grain boundaries from mathematical and numerical points of view.

In the first half of this talk, I will explain this problem and construct some efficient numerical scheme based on the method of fundamental solutions and the asymptotic uniform distribution method. I will also briefly survey the geometric numerical integration, which aims to construct a numerical scheme which inherits properties of the original problem in some discrete sense. In the second half of this talk, I will move on to the problem on grain boundaries and consider manifold-valued total variation flows. I will introduce spatially discretized total variation flow and construct a numerical scheme using the exponential map of the manifold. I will also present an energy dissipation property and convergence result.

Math-Fi seminar on 10 Oct.

2019.10.07 Mon up

Date: 10 Oct. (Thu.)
Place: W.W. 6th-floor, Colloquium Room
Time: 16:30-18:00
Speaker: Dan Crisan (Imperial College London)
Title: second lecture

Math-Fi seminar on 3 Oct.

2019.09.30 Mon up

Date: 3 Oct. (Thu.)
Place: W.W. 6th-floor, Colloquium Room
Time: 16:30-18:00
Speaker: Dan Crisan (Imperial College London)
Title: Modelling multi-period carbon markets using singular forward backward SDEs
Abstract:

I will introduce a model the evolution of emissions and the price of emissions allowances in a carbon market such as the European Union Emissions Trading System (EU ETSP). The model accounts for multiple trading periods (and phases) and multiple times at which compliance can occur. At the end of each trading period, the participating firms must surrender allowances for the emissions made during that period, but any excess allowances can be used for compliance in the following periods. We show that the multi-period allowance pricing problem is well-posed for various mechanisms linking the trading periods (such as banking, borrowing and withdrawals). The results are based on the analysis of a forward-backward stochastic differential equation with the following special characteristics: i. the forward and backward components are coupled, ii. the final condition is singular and iii. the forward component of the model is degenerate. I will also introduce an infinite period model, that is, a model for carbon market with a sequence of compliance times and no end date. I will show that, under appropriate conditions, the value function for the multi-period pricing problem converges, as the number of periods increases, to a value function for this infinite period model. This is joint work with Jean-Francois Chassagneux (Paris Diderot) and Hinesh Chotai (Citybank).

Math-Fi seminar on 12 Sep.

2019.09.09 Mon up

Date: 12 Sep. (Thu.)
Place: W.W. 6th-floor, Colloquium Room
Time: 16:30-18:00
Speaker: José Manuel Corcuera (Universitat de Barcelona)
Title: Contingent Convertibles (final lecture)

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