Seminar in EDP and Applied Mathematics

August 9th, 2023 – 14h (Brazil)

Streaming: Youtube Channel | SEMINARIO DE EDP E MATEMATICA APLICADA

Event

About Seminars

Our Online Seminar is one of the most important events in Brazil, it has been held since August 2020, every Wednesday at 2 pm, Brasília time, with a frequency of 14 days. Two 40-minute lectures are presented in each session. Our speakers are world-renowned mathematicians from Europe, the United States and South America.

Featured Talks & Speakers

Clément Mouhot

University of Cambridge, UK

14:00h – 14:40h

Quantitative Geometric Control in Kinetic Theory

We will start by a brief introduction to the so-called control theory in analysis of partial differential equations. This theory was initially developed for hyperbolic and parabolic problems (such as propagation of waves and diffusion of heat). However, many fundamental physical equations combine a transport hyperbolic term with a partially dissipative one: kinetic theory in particular presents such structure. We will then discuss a recent work (with F. Hérau, H. Hutridurga and H. Dietert) where we study a class of such equations for which the dissipation on the kinetic variable is active only on part of the spatial domain. We prove quantitative estimates of exponential stabilization under a geometric control condition reminiscent of control theory of wave equations. The proof relies on a new approach to hypocoercivity based on trajectories and quantitative divergence inequalities.

Yuri Thamsten

Vector Trading LLC, Chicago IL, US

14:50h – 15:30h

Optimal trade execution strategies: general models, the strict
problem, and ergodic approximations.

We present a model for optimal execution in which both volatility and liquidity are stochastic.
Our assumption is that a multi-dimensional Markov diffusion drives these processes. In our model, the market is frictional. Particularly, the trader incurs a instantaneous price impact.In this connection, we consider concave-shaped or linear limit order books.

In the regularized setting, meaning we do not necessarily enforce strict execution, we characterize the value function as the unique continuous viscosity solution to the corresponding HJB. We provide this result using appropriate an monotonicity and fixed point arguments.From our method, an iterative numerical algorithm follows for approximating the regularized solution. Then, further proceeding with the monotonicity arguments, we obtain the solution of the optimal strict execution problem as a (singular) limit of its regularized counterparts.Particularly, we guarantee a good numerical approximation for the strict execution problem —
to our knowledge, for the first time in the literature.
Subsequently, we specialize the Markov diffusion to be a fast mean-reverting one. We assess this
hypothesis by using high-frequency financial data. We provide a novel bagging methodology for
estimating the random liquidity model parameters, and also employ noise-robust methods for
estimating the stochastic volatility. Working under this ergodic framework, we derive a leadingorder approximation for the optimal solutions we studied before, and also get a first-order
correction. We provide numerical illustrations and accuracy results for our approximations.

About Organization

Juan Limaco – UFF – Brazil (Coordenador);
Mauro Rincon – UFRJ – Brazil
Max Souza – UFF – Brazil;
Sandra Malta – LNCC – Brazil
Marcelo Cavalcanti – UEM – Brazil;
Rui Almeida – UBI – Portugal
Roxana Lopez – UNMSM – Peru;
Diego Souza – U Sevilla – España;
Mauricio Sepulveda – UdeC – Chile;
Roberto Capistrano – UFPE – Brazil.