News&Events

Math-Fi seminar on 20 Apr.

2023.04.17 Mon up
  • Date: 20 Apr. (Thu.)
  • Place: W.W. 6th-floor, Colloquium Room and on the Web (Zoom)
  • Time: 16:30 – 18:00
  • Speaker: Thomas Cavalazzi (Université de Rennes 1)
  • Title: Quantitative weak propagation of chaos for McKean-Vlasov SDEs driven by $\alpha$-stable  processes
  • Abstract: 
In this talk, we will deal with McKean-Vlasov Stochastic Differential Equations (SDEs) driven by $\alpha$-stable processes, with $\alpha \in (1,2)$. We make Hölder-type assumptions on the coefficients, with respect to both space and measure variables. 
We will study the associated semi-group, acting on functions defined on the space of probability measures, through the related backward Kolmogorov Partial Differential Equation (PDE), which describes its dynamics. 
We will focus in particular on its regularizing properties. 
The study relies on differential calculus for functions defined on the space of measures, and on Itô’s formula along flows of marginal distributions of jump processes defined with Poisson random integrals. 
We will finally use the preceding tools to prove quantitative weak propagation of chaos for the mean-field interacting particle system associated with the McKean-Vlasov SDE.

Math-Fi seminar on 6 Apr.

2023.04.04 Tue up
  • Date: 6 Apr. (Thu.)
  • Place: W.W. 6th-floor, Colloquium Room and on the Web (Zoom)
  • Time: 16:30 – 18:00
  • Speaker: Tommaso Mariotti (Scuola Normale Superiore di Pisa)
  • Title: Coding examples with Python

Math-Fi seminar on 30 Mar.

2023.03.29 Wed up
  • Date: 30 Mar. (Thu.)
  • Place: W.W. 6th-floor, Colloquium Room and on the Web (Zoom)
  • Time: 11:00 – 12:30
  • Speaker: Xunyu Zhou (Columbia University)
  • Title: Reinforcement Learning in Continuous Time
  • Abstract:
In this talk I will report some of the latest developments in model-free, 
data-driven reinforcement learning in continuous time with possibly continuous state and action spaces, 
including exploratory formulation, policy evaluation, policy gradient and q-learning. 
Time permitting I will also present applications to portfolio selection.
 

Math-Fi seminar on 23 Mar.

2023.03.22 Wed up
  • Date: 23 Mar. (Thu.)
  • Place: W.W. 6th-floor, Colloquium Room and on the Web (Zoom)
  • Time: 15:30 – 19:00
 
Part 1: 15:30 PM – 17:00 PM 
  • Speaker: Tommaso Mariotti (Scuola Normale Superiore di Pisa)
  • Title: Financial econometrics in high-frequency data
  • Abstract: 
The rise of high-frequency data opened new opportunity, but at the same time poses new challenges in the last decades. Focusing in particular on non-parametric estimation of volatility of stochastic processes, the presence of market microstructure noise is analysed, considering its influence on the consistency of traditional non-parametric estimators such as the realized volatility. Several models for noise are presented, considering their connections with the microstructure models presented in the previous talk. Consistent estimation of volatility in presence of noise is discussed, together with the issue of assessing the presence of noise in financial data. The presence of jumps is discussed analogously, presenting techniques to spot and manage discontinuities in the data while performing volatility estimation.
 
Part 2: 17:30 – 19:00
  • Speaker: Ngo Hoang Long (Hanoi National University of Education)
  • Title:Simulation of McKean-Vlasov SDE’s
  • Abstract:
In this talk, we introduce a tamed-adaptive approximation scheme for McKean-Vlasov SDEs with super-linear coefficients. 
We consider the rates of convergence of the new scheme in $L^p$-norm on both finite and infinite time intervals. 
 

Math-Fi seminar on 7 Mar.

2023.03.06 Mon up
  • Date: 7 Mar. (Tue.)
  • Place: W.W. 6th-floor, Colloquium Room and on the Web (Zoom)
  • Time: 17:30-19:00
  • Speaker: Hiroshi Kawabi (Keio University)
  • Title: A graph discretized approximation of diffusions with drift and killing on a complete Riemannian manifold
  • Abstract: Please click here

Math-Fi seminar on 2 Mar.

2023.03.01 Wed up
  • Date: 2 Mar. (Thu.)
  • Place: W.W. 6th-floor, Colloquium Room and on the Web (Zoom)
  • Time: 14:30 – 18:00

Part 1: 14:30 – 16:00 
  • Speaker: Benjamin Poignard (Osaka University)
  • Title: Sparse M-estimators in semi-parametric copula models
  • Abstract: Please click here
 
Part 2: 16:30 – 18:00
  • Speaker: Xiaoming Song (Drexel University)
  • Title: Fractional stochastic wave equation driven by a Gaussian noise rough in space
  • Abstract: Please click here
 

Math-Fi seminar on 28 Feb.

2023.02.27 Mon up
  • Date: 28 Feb. (Tue.)
  • Place: W.W. 6th-floor, Colloquium Room and on the Web (Zoom)
  • Time: 17:30-19:00
  • Speaker: Kotaro Hata (Hokkaido University)
  • Title: Uniform Weak Convergence to Additive Processes
  • Abstract:
In 1929, Finetti introduced the concept of an infinitely divisible distribution. It’s been developed by many probabilists and now plays an important role in probability theory. In this talk, I will introduce the relationship between infinitely divisible distributions and additive processes and between infinitely divisible distributions and infinitesimal triangular arrays. After that, we will give a necessary and sufficient condition for a sequence of stochastic processes which is generated by an infinitesimal triangular array to weakly converge an additive process uniformly. In the end, I will give some propositions and examples as a special case of main results. This talk is based on a joint work with Hasebe Takahiro.

Math-Fi seminar on 19 Jan.

2023.01.18 Wed up
  • Date: 19 Jan. (Thu.)
  • Place: W.W. 6th-floor, Colloquium Room and on the Web (Zoom)
  • Time: 18:00-19:30
  • Speaker: Tai-Ho Wang (Baruch College)
  • Title: Entropy regularized robust optimal order execution
  • Abstract:
Order execution, a mission that algorithmic trading departments and execution brokerage agencies embark on regularly, is cast as an entropy-regularized robust optimal control problem. During the course of executing a large order of significant amount, the agent faces with not only the risk of price impact that his own execution would incur towards the transaction price but also the liquidity and uncertainty of the market. The agent’s goal is to maximize an objective functional associated with his profit-and-loss of trading and simultaneously minimize the exeuction risk. It is documented that “a liquid market is one which is almost infinitely tight, which is not infinitely deep, and which is resilient enough so that prices eventually tend to their underlying value”. As such, we model the market’s liquidity and uncertainty by the principle of least relative entropy associated with the market volume. The problem of order execution is thus turned into a relative entropy-regularized (Bayesian) stochastic differential game. Standard argument of dynamic programming applies in this setting which yields that the value function of the differential game satisfies a “Bayesian” Hamilton-Jacobi-Isaacs (HJI) equation. Under the assumptions of linear-quadratic model with Gaussian prior, the Bayesian HJI equation reduces to a system of Riccati and linear differential equations. Further imposing constancy of the corresponding coefficients, the system of differential equations can be solved in closed form, resulting in analytical expressions for optimal strategy and trajectory as well as the posterior distribution of market volume. 
In conclusion, numerical examples, comparisons and discussions of the optimal strategy to conventional trading strategies are demonstrated.

Math-Fi seminar on 5 Dec.

2022.12.04 Sun up
  • Date: 5 Dec. (Mon.)
  • Place: On the Web (Zoom)
  • Time: 10:30-12:00
  • Speaker: Pei-Chun Su (Duke University)
  • Title: Optimal shrinkage of singular values under noise with separable covariance & Its application to fetal ECG analysis
  • Abstract:
​High dimensional noisy dataset is commonly encountered in many scientific fields, and a critical step in data analysis is denoising. Under the white noise assumption, optimal shrinkage has been well developed and widely applied to many problems. However, in practice, noise is usually colored and dependent, and the algorithm needs a modification. We introduce a novel fully data-driven optimal shrinkage algorithm when the noise satisfies the separable covariance structure. The novelty involves a precise rank estimation and an accurate imputation strategy. In addition to showing theoretical supports under the random matrix framework, we show the performance of our algorithm in simulated datasets and apply the algorithm to extract fetal electrocardiogram from the benchmark trans-abdominal maternal electrocardiogram, which is a special single channel blind source separation challenge.
 

Math-Fi seminar on 1 Dec.

2022.12.01 Thu up
  • Date: 1 Dec. (Thu.)
  • Place: W.W. 6th-floor, Colloquium Room and on the Web (Zoom)
  • Time: 16:30-18:00
  • Speaker: Ju Yi Yen (University of Cincinnatti)
  • Title: Mathematical analysis of automated market makers
  • Abstract:
Automated market makers (AMMs) are examples of Decentralized Finance systems. Nowa- days, AMMs are dominated by the Constant Function Market Makers (CFMMs). CFMMs pool liquidity from its takers and providers, and set the relative prices of the two assets within the pool by a mathemat- ical formula. The relative price is determined by the reserves of the two assets in the pool. Notice that the assets in the liquidity pool are risky assets, their performances are impacted by the market risk. In this talk, we describe the stochastic process used for modeling the relation between the pool price and the corresponding market price for assets traded via CFMMs, and present limit theorems of this stochastic process. Our results are deduced from properties of the Brownian motion and its local time process.

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