セミナー

Math-Fi seminar on 24 Jun.

2021.06.23 Wed up
  • Date: 24 Jun. (Thu.)
  • Place: On the Web
  • Time: 16:30 – 18:00
  • Speaker: Maria Elvira Mancino (University of Florence)
  • Title: Volatility and higher order covariances estimation for identifying financial instability conditions and computing hedging Greeks
  • Abstract:
I would present the most recent papers with Simona, both of them use the same mathematical instruments for different applications. Further, it is based on some ideas presented in the paper with Malliavin  “”Harmonic analysis methods for nonparametric estimation of volatility: theory and applications””. In  Proceedings of the International Symposium “Stochastic Processes and Applications to Mathematical Finance” 2005 at Ritsumeikan University, World Scientific (2006).  Eds. J.Akahori, S.Ogawa, S.Watanabe.

Math-Fi seminar on 17 Jun.

2021.06.17 Thu up
  • Date: 17 Jun. (Thu.)
  • Place: On the Web
  • Time: 16:30 – 18:00
  • Speaker: Olivier Menoukeu Pamen (African Institute of Mathematical Sciences and University of Liverpool)
  • Title:Takagi type functions and dynamical systems: the smoothness of the SBR measure and the existence of local time
 

Math-Fi seminar on 10 Jun.

2021.06.09 Wed up
  • Date: 10 Jun. (Thu.)
  • Place: On the Web
  • Time: 16:30 – 18:00
  • Speaker: Pierre Bras (Sorbonne University, LPSM)
  • Title: Convergence rates of Gibbs measures with degenerate minimum
  • Abstract:
We study convergence rates of Gibbs measures, with density $\pi_t(dx) \propto e^{-f(x)/t} dx$, as $t \to 0$ and where $f: \mathbb{R}^d \to \mathbb{R}$ admits a unique global minimum at $x^\star$. If the Hessian matrix $\nabla^2 f(x^\star)$ is positive definite then a Taylor expansion up to order 2 shows that $\pi_t$ converges to the Dirac measure $\delta_{x^\star}$ at speed $\sqrt{t}$.
We focus on the case where the Hessian of $f$ is not definite at $x^\star$. We assume instead that the minimum is strictly polynomial and we give a higher order nested expansion of $f$ at $x^\star$. We give an algorithm yielding such decomposition, in connection with Hilbert’s $17^{th}$ problem. We then give the rate of convergence of $\pi_t$ using this expansion.
Our work can be applied to stochastic optimization, where the Gibbs measure $\pi_t$ with small $t$ is used as an approximation of the minimizer of $f$.
 

立命館大学数理工学セミナー（2021年5月31日（月））

2021.05.27 Thu up
<<立命館大学幾何学セミナー>>

日時：2021年5月31日（月） 16:30～18:00

タイトル：
プラズマ乱流が励起する非線形構造と核融合閉じ込めへの応用

講演者：
小菅 佑輔 （九州大学）

アブストラクト：
本セミナーでは、世界各国で精力的に進められている核融合研究について紹介し、その閉じ込め性能を理解する上で必要となるプラズマ乱流研究について解説する。特に、プラズマ乱流が駆動する非線形構造に焦点をあて、我々のグループで進めている励起過程の理解や制御を目指した研究について紹介する。これらの研究を支える代表的なモデルについて触れ、非線形Schroedinger方程式に基づく非線形構造励起の研究や、ハミルトン構造を有する方程式系（Vlasov方程式や２次元乱流系を記述するCharney-Hasegawa-Mima方程式や運動論的乱流を記述するVlasov 方程式）に基づく緩和研究などを紹介する。

開催方法：Zoom配信での開催です．

問い合わせ先：立命館大学理工学部数理科学科 多羅間 大輔

Math-Fi seminar on 20 May

2021.05.19 Wed up
  • Date: 20 May (Thu.)
  • Place: On the Web
  • Time: 16:30 – 18:00
  • Speaker: Libo Li (University of New South Wales)
  • Title: Random times and RBSDEs
  • Abstract:
In this talk, we will discuss three related topics. The first is the additive and multiplicative representation of the survival process of a finite honest time. We show that the survival process can be expressed as drawdown and relative drawdown of some optional supermartingale with continuous running supremum, and we recover the Madan-Roynette-Yor option pricing formula involving  the last passage times of zero for optional semimartingales of class-sigma. The second is the construction of random time, where we extend using, multiplicative systems, the Madan-Roynette-Yor to all positive optional supermartingale and apply our results to construct random time with a given survival process. Finally motivated by the arbitrage-free pricing of European and American style contracts with the counterparty credit risk, we investigate the well-posedness of BSDE and RBSDE in the progressive enlargement of a reference filtration with a random time through the method of reduction.

Math-Fi seminar on 13 May

2021.05.13 Thu up
  • Date: 13 May (Thu.)
  • Place: On the Web
  • Time: 16:30 – 18:00
  • Speaker: Lihu Xu (University of Macau)
  • Title: Stein’s method: stable law approximation
  • Abstract:
In this talk, we will consider the stable law approximation by Stein’s method in Wasserstein-1 distance and derive a discrepancy form of the stable type central limit theorem (CLT) under appropriate conditions. The main ingredient in the proof is by solving a Stein’s equation, decomposing fractional Laplacian and using a leave-one-out argument.  From the discrepancy form,  we can obtain the optimal convergence rate of stable CLT.

Math-Fi seminar on 22 Apr.

2021.04.21 Wed up
  • Date: 22 Apr. (Thu.) 
  • Place: On the Web 
  • Time: 16:30 – 18:00
  • Speaker: Jorge González Cázares (University of Warwick)
  • Title: Recovering Brownian and jump parts from high-frequency observations of a Lévy process
  • Abstract:
We introduce two general non-parametric methods for recovering paths of the Brownian and jump components from high- frequency observations of a Lévy process, both methods yield the same polynomial rate of convergence dependent on the  Blumenthal-Getoor index. The first procedure relies on reordering of independently sampled normal increments and thus avoids tuning parameters. The functionality of this method is a consequence of the small time predominance of the Brownian component, the presence of exchangeable structures, and fast convergence of normal empirical quantile functions. The second procedure  filters the increments and compensates with the final value, requiring a carefully chosen threshold.

立命館大学幾何学セミナー（2021年4月23日（金））

2021.04.20 Tue up
<<立命館大学幾何学セミナー>>

日時：2021年4月23日（金） 16:30～18:00

タイトル：Long-time asymptotics of random walks on covering graphs with groups of polynomial volume growth

講演者：難波 隆弥（立命館大学）

アブストラクト：
We discuss central limit theorems (CLTs) for non-symmetric random walks on covering graphs of finite graphs whose covering transformation groups are groups of polynomial volume growth. By realizing the covering graph into a certain nilpotent Lie group through a discrete harmonic map, we show that the limiting semigroup is generated by the sub-Laplacian with a non-trivial linear drift on the nilpotent Lie group equipped with the Albanese metric. Furthermore, under the centered condition, we establish a functional CLT (i.e., Donsker-type invariance principle) in a Hölder space over the nilpotent Lie group by employing the theory of rough paths. As a refinement of the CLT, we also establish the Edgeworth expansion of the random walk even if the random walk is non-symmetric. A part of this talk is based on joint work with Satoshi Ishiwata (Yamagata) and Hiroshi Kawabi (Keio). 

開催方法：Zoom配信での開催です．

問い合わせ先：立命館大学理工学部数理科学科 多羅間 大輔

Math-Fi seminar on 15 Apr.

2021.04.15 Thu up
  • Date: 15 Apr. (Thu.) 
  • Place: On the Web 
  • Time: 16:30 – 18:00
  • Speaker: Tai-Ho Wang (Baruch College)
  • Title: Dynamic optimal execution under price impact with inventory cost: a heterogeneous characteristic time scales approach
  • Abstract:
We generalize the classical Almgren-Chriss model of price impact by adding an extra feature that models the market makers’ impact to the transaction price by aggregated Ornstein-Uhlenbeck processes. During execution of a meta order, market makers are assumed to mean revert their positions to certain preassigned capacities. Once the execution terminates, the market makers revert their positions back to zero. The expected price path post TWAP (time weighted average price) execution reverts to a price level higher than price before the TWAP execution. Should there be no contribution from the market maker, the model recovers the classical Almgren-Chriss model. The execution problem faced by investor can be recast as a possibly infinite dimensional stochastic control problem, which in general is neither Markovian nor semimartingale. However, the problem remains linear-quadratic, as a result, we are able to derive, and consequently obtain the optimal trading strategies, a system of Riccati equations that characterizes the value function of the stochastic control problem. Numerical examples will be presented to illustrate the implementation of the resulting optimal execution strategy under the proposed model.
The talk is based on a joint work with Xue Cheng and Marina Di Giacinto.

Math-Fi seminar on 9 Apr.

2021.04.08 Thu up
  • Date: 9 Apr. (Fri.) 
  • Place: On the Web 
  • Time: 16:30 – 18:00
  • Speaker: Tomonori Nakatsu
  • Title: Stochastic delay equationの解の密度関数の評価と伊藤Taylor展開
  • Abstract:
本発表ではまず、Stochastic delay equationの解の密度関数の下からの評価に関する結果を紹介する。次に、Stochastic delay equationに対する伊藤Taylor展開について述べる。両トピックは独立した内容であるが、ともにMalliavin解析が重要な役割を果たす。
 

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