Seminars

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.

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

Math-Fi seminar on 25 Mar.

2021.03.24 Wed up
  • Date: 25 Mar. (Thu.) 
  • Place: On the Web
  • Time: 16:30  – 18:00 
  • Speaker: Toshiyuki Nakayama (MUFG Bank, Ltd.)
  • Title: Convergence speed of Wong-Zakai approximation for stochastic PDEs (Joint work with Stefan Tappe)
  • Abstract: 
We talk about semi-linear stochastic differential equation (SPDE) driven by finite dimensional Brownian motion. There are a few results regarding convergence rates, such as for a second-order parabolic type (Gyöngy and Shmatkov (2006), Gyöngy and Stinga (2013)) and for the infinitesimal generator of a compact and analytic semigroup (Hausenblas(2007)).
Our goal is to establish a convergence rate without imposing restrictions on the generator, that is, the generator is allowed to be the infinitesimal generator of an arbitrary strongly continuous semigroup.
Finally, we will introduce an application example for SPDE called HJMM that appears in mathematical finance.
Today’s talk is based on a co-authored paper with Stefan Tappe “ Wong-Zakai approximations with convergence rate for stochastic partial differential equations ”, 
STOCHASTIC ANALYSIS AND APPLICATIONS 2018, VOL. 36, NO. 5, pp. 832–857.

Math-Fi seminar on 18 Mar.

2021.03.18 Thu up
  • Date: 18 Mar. (Thu.) 
  • Place: On the Web
  • Time : 16:30 - 18:00 
  • Speaker: Noufel Frikha (Paris VII)
  • Title: On Some new integration by parts formula for finance and their Monte Carlo simulation
  • Abstract:
​In this talk, I will present some new integration by parts (IBP) formulae for the marginal law at a given time maturity of killed diffusions as well as a class of stochastic volatility models with unbounded drift. Relying on a perturbation argument for Markov processes, our formulae are based on a simple Markov chain evolving on a random time grid for which we develop a tailor-made Malliavin calculus. Though such formulae could be further analyzed to study fine properties of the associated densities, our main motivation lies in their numerical approximation. Indeed, we show that an unbiased Monte Carlo path simulation method directly stems from our formulae so that it can be used in order to numerically compute with optimal complexity option prices as well as their sensitivities with respect to the initial values, the so-called Greeks, namely the Delta and Vega, for a large class of non-smooth European payoff. Numerical results are proposed to illustrate the efficiency of the method.
 
This talk is based on two joint works: with Arturo Kohatsu-Higa (Ritsumeikan university) and Libo Li (New South Wales university) on the one hand, with Junchao Chen (universit ́e de Paris) and Houzhi Li (universit ́e de Paris) on the other hand.

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