The Speakers

Here are the speakers :

Lucas Rey

PhD candidate - Ceremade

Title: Forêts et arbres couvrant aléatoire en régime critique et presque critique

Tommy Rakoto Endor

PhD candidate - Ceremade

Title: Benign non convexity of the Burer Monteiro factorization

Othmane Zarhali

PhD candidate - Ceremade/CNRS

Title: The Log S-fbm Nested factor model

Abstract: The Nested factor model was introduced by Bouchaud and al. where the asset returns are explained by common factors representing the market economic sectors and residuals (noises) sharing with the factors a common dominant volatility mode in addition to the idiosyncratic mode proper to each residual. This construction infers that the factors-residuals log volatilities are correlated. Here, we consider the case of a single factor where the only dominant common mode is a S-fbm process with Hurst exponent H ≃ 0.11 and the residuals having in addition to the previous common mode idiosyncratic components with Hurst exponents H ≃ 0. The reason for considering this configuration is two fold: preserve the Nested factor model’s characteristics introduced by Bouchaud and al. and propose a framework through which the stylized fact reported by Peng and al. is reproduced, where it has been observed that the Hurst exponents of stock indices are large as compared to those of individual stocks. In this work, we show that the Log S-fbm Nested factor model’s construction leads to a Hurst exponent of single stocks being the ones of the idiosyncratic volatility modes, and the Hurst exponent of the index being the one of the common volatility mode. Furthermore, we propose a statistical procedure to estimate the Hurst factor exponent from the stock returns dynamics together with theoretical guarantees, with good results in the limit where the number of stocks N → +∞. Last but not least, we show that the factor can be seen as an index constructed from the single stocks weighted by specific coefficients.

Aaminata Ndiaye

PhD candidate - Ceremade

Title: An introduction on causal graphical modeling

Yijun Wan

Postdoc researcher - Ceremade

Title: Neural network compression with heavy-tailed SGD

Ivan Novikov

PhD candidate - Ceremade

Title: Zero-Sum Stochastic Games with Vanishing Stage Duration and Public Signals

Lucas Davron

PhD candidate - Ceremade

Title: An introduction to control of PDEs

Abstract: This presentation aims at introducing control theory for PDEs with the internal control of the heat equation. First the heat equation is introduced and several of its features are recalled. Second we show the duality between controllability and observability using the so-called HUM method with a "functional analysis" proof. Finally we compare the features of the heat equations with its controllability properties. If time permits I will present the hump's trick, allowing one to deduce boundary controllability from internal controllability.

Amal Omrani

PhD candidate - Ceremade

Title: A new approach for Leland's strategies in financial market models with transaction costs

Abstract: For several decades, the no-arbitrage (NA) conditions and martingale mea- sures have been central to determining fair prices for financial products. The Black-Scholes model, introduced in the early 1970s, provided a foun- dational framework for valuing European-style options under NA conditions. However, this model has its limitations, as it assumes that prices follow a ge- ometric Brownian motion with constant volatility and does not account for transaction costs. Leland (1985) proposed an approach for pricing under proportional transac- tion costs through periodic revisions of the hedging portfolio, using a modified Black-Scholes formula with adjusted volatility to account for market frictions. The portfolio value of this approach asymptotically replicates the payoff as the number of revisions approaches infinity, but the replication price limit of the payoff is essentially the ”buy and hold” price. Furthermore, by using the Black- Scholes model, this approach continues to assume the same price modeling and NA conditions. Here, I present a new approach to Leland’s strategies with transaction costs, which does not assume a specific price process model or rely on the risk- free probability measure. This method aims to provide a more flexible and realistic framework for pricing in the presence of market frictions.

Elise Devey

PhD candidate - Ceremade/Inria

Title: McKean-Vlasov optimal control problem and its application to electricity management

Abstract: This talk serves as an introduction to the Optimal Control of SDEs of McKean-Vlasov type. We begin by introducing the basics of stochastic control, followed by presenting two reformulations of the problem: one using the Hamilton-Jacobi equation from an analytical perspective and the other using Forward-Backward Stochastic Differential Equations (FBSDE) from a probabilistic perspective. Next, we explore the Mean Field Control (MFC) problem, or Optimal Control of SDEs of McKean-Vlasov type, which is distinguished by the presence of the distribution of the controlled state in the coefficients. To address this, we develop differential calculus in the space of measures and extend the previously established results. Finally, we apply this theoretical framework to managing flexibility in the electricity network, aiming to ease the constraint of maintaining equilibrium between supply and demand.

Cesar Romero Mora

PhD candidate - Ceremade

Title: A proof of the Weak KAM theorem

Cristobal Loyola

PhD candidate - LJLL

Title: Global propagation of analyticity and UCP for nonlinear waves

Raphael Prunier

Postdoc researcher - Ceremade

Title: Free boundary problems in the optimal control of reaction-diffusion equations

Abstract: The aim of the talk is to give an overview of the specific problems and tools related to the study of optimal control problems in reaction-diffusion models. After presenting the famous Fisher-KPP model, we introduce the notion of survival ability of a population. As often in optimal control problems, the optimization of this quantity provides bang-bang minimizers; a perhaps more specific feature regards the fact that the associated sets can be written as su- perlevel sets of the related eigenfunction, which enables to interpret the Euler- Lagrange equation of the problem as a free boundary PDE. In the final part of the talk we provide a two-dimensional regularity result for the free boundary due to Chanillo, Kenig and To, and quickly sketch the blow-up analysis which is employed in its proof.

Quentin François

PhD candidate - Ceremade

Title: A positive formula for the product of conjugacy classes on the unitary group

Abstract: We study the convolution product of two conjugacy classes of the unitary group 𝑈𝑛 described by a probability distribution on the space of central measures which admits a density. Relating the convolution to the quantum Littlewood-Richardson coefficients and using recent results describing those coefficients, we give a positive formula for this density. In the same flavor as the hive model of Knutson and Tao, this formula is given in terms of a subtraction-free sum of volumes of explicit polytopes.

Henri Surugue

PhD candidate - MICS

Title: Probabilistic tools in Computational Social Choice and Game Theory: a broad introduction and concrete examples

Abstract: In this talk, we present a very large view of probabilistic tools used in computational social choice and game theory. We will start with a broad introduction of the context in which we may need such approaches. Then, we will consider 3 problems from voting theory: the problem of poll manipulation in large political elections, the question of finding consensual voting rules facing impossibility theorems and finally the prediction problem with strategic voters.

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