Graph theory, non-linear dynamic systems, sparse dynamics, finite-sample and asymptotic theory, model regularization and complexity reduction.
I am currently a PhD candidate in mathematics on the topic of dynamic processes of correlation matrices based on graphical vines.
I worked on processes of partial correlations parameterized by underlying graphs called vines. This approach fosters sparsity and alows for the dependence modeling of high-dimensional random vector. I extensively studied its asymptotic properties and probabilisitc properties (stationarity and ergodicity).
I currently work on penalized empirical processes and focus on the asymptotic properties of the Sparse Group Lasso and its adaptive version (inclusion of a first step weight penalizing the coefficients differently). I focus on the oracle property both in a simple and double asymptotic framework, where the model complexity grows with the sample size.
October 2014-Present: PhD student in Applied Mathematics, Center for Research in Economics and Statistics (CREST) and Paris Dauphine University (CEREMADE)
2012-2014: ENSAE ParisTech, Statistician-Economist Program.
2012: Master Modeling and Mathematical Methods in Economics and Finance (DEA MMME), University Paris 1 Panthéon-Sorbonne.
2009-2012: ESCP Europe, Master in Management.
2009-2011: University Paris 1 Panthéon-Sorbonne, Bachelor and Master 1 in Applied Mathematics.
May 2015 - Present: Consultant in quantitative research at Louis Bachelier Institute, Paris, France.
June 2014 - September 2014: Intern in quantitative research, Financial Engineering Team at risklab Gmbh, Munich, Germany.
2012 - 2013: Part-time intern in quantitative research at Europlace Institute of Finance, Paris, France.
Winter 2017: dynamic statistical models and hidden variables, Osaka University
Work in progress
Sparse dynamic variance-covariance matrix processes, with Jean-David Fermanian (CREST-ENSAE).
Abstract: "This paper proposes a general framework for penalized convex empirical criteria and a new version of the Sparse-Group LASSO (SGL, Simon and al., 2013), called the adaptive SGL, where both penalties of the SGL are weighted by preliminary random coefficients. We explore extensively its asymptotic properties and prove that this estimator satisfies the so-called oracle property (Fan and Li, 2001), that is the sparsity based estimator recovers the true underlying sparse model and is asymptotically normally distributed. Then we study its asymptotic properties in a double-asymptotic framework, where the number of parameters diverges with the sample size. We show by simulations that the adaptive SGL outperforms other oracle-like methods in terms of estimation precision and variable selection."
Vine-GARCH process: Stationarity and Asymptotic Properties, with Jean-David Fermanian (CREST-ENSAE):
Abstract: "We provide conditions for the existence and the uniqueness of strictly stationary solutions of the Vine-GARCH process. The proof is based on Tweedie’s (1988) criteria, after rewriting the Vine-GARCH process as a nonlinear Markov chain. Furthermore, we provide asymptotic results of the estimators obtained by the quasimaximum likelihood method. We prove the weak consistency and asymptotic normality of the quasi-maximum likelihood estimator obtained in a two-step procedure."
Dynamic Processes of Asset Correlation, with Jean-David Fermanian (CREST-ENSAE):
Abstract: " We develop a new method for generating dynamics of conditional correlation matrices. These correlation matrices are parameterized by a subset of their partial correlations, whose structure is described by a set of undirected graphs called "vine''. Partial correlation processes can be specified separately and arbitrarily, providing a new family of very flexible multivariate GARCH processes, called ``vine-GARCH'' processes. We estimate such models by quasi-maximum likelihood and we study the corresponding asymptotic theory. We compare our models with some DCC-type specifications through some simulated experiments and we evaluate their empirical performances."
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