News&Events

Math-Fi seminar on 22 Jul.

2021.07.21 Wed up
  • Date: 22 Jul. (Thu.)
  • Place: On the Web
  • Time: 16:30 – 18:00
  • Speaker: Lorenzo Marino (Université d’Evry Val d’Essonne, University of Pavia)
  • Title: Weak Regularization by Degenerate Lévy noise and Applications
  • Abstract:
In this talk, we briefly present the arguments of the PhD thesis: “Weak Regularization by Degenerate Lévy noise and Applications”. After a general introduction on the regularization by noises phenomena and the motivations behind this work, we start by showing the Schauder estimates, a useful analytical tool for the wellposedness of SDEs, for two different classes of integro-differential equations whose coefficients lie in suitable anisotropic Hölder spaces with multi-indices of regularity. The first one focuses on non-linear dynamics controlled by an α-stable operator acting only on the first component. To deal with the non-linear perturbation, we also need some subtle controls on Besov norms. As an extension of the first one, we also present the Schauder estimates associated with a degenerate Ornstein-Uhlenbeck operator driven by a larger class of α-stabletype operators, like the relativistic or Lamperti stable ones. The proof of this result relies instead on a precise analysis of the behaviour of the associated Markov semigroup between anisotropic Hölder spaces and some interpolation techniques. Exploiting a backward parametrix approach, we finally prove the weak wellposedness of the associated degenerate chain of SDEs. As a by-product of our method, Krylov-type estimates on the canonical solution process are also presented. Time permitting, we conclude by showing through suitable counter-examples that there exists an (almost) sharp threshold for the regularity exponents that ensure the weak well-posedness for the SDE.
 

Math-Fi seminar on 8 Jul.

2021.07.07 Wed up
  • Date: 8 Jul. (Thu.)
  • Place: On the Web
  • Time: 16:30 – 18:00
  • Speaker: Shota Nakamura (Waseda University)
  • Title: 長期記憶性を持つサープラスの破産確率の推定

Math-Fi seminar on 1 Jul.

2021.06.30 Wed up
  • Date: 1 Jul. (Thu.)
  • Place: On the Web
  • Time: 16:30 – 18:00
  • Speaker: Roger Pettersson (Linnaeus University)
  • Title: Epidemic modeling on microscopic, macroscopic and mesoscopic scale: the Kurtz’ approach
 

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 $f$.
 

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.

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.

« Prev | Next »