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5 results on '"Labart, Céline"'

1. Lightweight Curvature Estimation on Point Clouds with Randomized Corrected Curvature Measures

Author

Lachaud, Jacques-Olivier, Coeurjolly, David, Labart, Céline, Romon, Pascal, Thibert, Boris, Laboratoire de Mathématiques (LAMA), Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry])-Centre National de la Recherche Scientifique (CNRS), Origami (Origami), Laboratoire d'InfoRmatique en Image et Systèmes d'information (LIRIS), Université Lumière - Lyon 2 (UL2)-École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Université Lumière - Lyon 2 (UL2)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), Laboratoire Analyse et Mathématiques Appliquées (LAMA), Université Paris-Est Créteil Val-de-Marne - Paris 12 (UPEC UP12)-Centre National de la Recherche Scientifique (CNRS)-Université Gustave Eiffel, Equations aux Dérivées Partielles (EDP), Laboratoire Jean Kuntzmann (LJK), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA), ANR-22-CE46-0006,StableProxies,Traitement numérique stable de la géométrie et calcul haute-performance sur des données géométriques hétérogènes(2022), and ANR-11-LABX-0025,PERSYVAL-lab,Systemes et Algorithmes Pervasifs au confluent des mondes physique et numérique(2011)

Subjects
Computing methodologies → Shape analysis, [INFO.INFO-CG]Computer Science [cs]/Computational Geometry [cs.CG]
Abstract

International audience; The estimation of differential quantities on oriented point cloud is a classical step for many geometry processing tasks in computer graphics and vision. Even if many solutions exist to estimate such quantities, they usually fail at satisfying both a stable estimation with theoretical guarantee, and the efficiency of the associated algorithm. Relying on the notion of corrected curvature measures [LRT22, LRTC20] designed for surfaces, the method introduced in this paper meets both requirements. Given a point of interest and a few nearest neighbours, our method estimates the whole curvature tensor information by generating random triangles within these neighbours and normalising the corrected curvature measures by the corrected area measure. We provide a stability theorem showing that our pointwise curvatures are accurate and convergent, provided the noise in position and normal information has a variance smaller than the radius of neighbourhood. Experiments and comparisons with the state-of-the-art confirm that our approach is more accurate and much faster than alternatives. The method is fully parallelizable, requires only one nearest neighbour request per point of computation, and is trivial to implement.

Published
2023
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2. SIMULATION OF MCKEAN-VLASOV BSDES BY WIENER CHAOS EXPANSION

Author

Acary-Robert, Céline, Briand, Philippe, Ghannoum, Abir, Labart, Céline, Laboratoire de Mathématiques (LAMA), and Centre National de la Recherche Scientifique (CNRS)-Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry])

Subjects
[MATH.MATH-PR]Mathematics [math]/Probability [math.PR], Mathematics::Probability
Abstract

We present an algorithm to solve McKean-Vlasov BSDEs based on Wiener chaos expansion and Picard's iterations and study its convergence. This paper extends the results obtained by Briand and Labart in [BL14] when standard BSDEs were considered. Here we are faced with the problem of the approximation of the law of (Y, Z) in the driver, that we solve by using a particle system. In order to avoid solving a system of BSDEs, which would not be feasible in practice, we use the same particles to approximate the law of (Y, Z) and to compute Monte Carlo approximations. This leads to an algorithm which doesn't cost more than the standard one.

Published
2019

3. A Parallel Algorithm for solving BSDEs - Application to the pricing and hedging of American options

Author

Labart, Céline, Lelong, Jérôme, Laboratoire de Mathématiques (LAMA), Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry])-Centre National de la Recherche Scientifique (CNRS), Financial mathematics (MATHFI), Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-École des Ponts ParisTech (ENPC)-Université Paris-Est Créteil Val-de-Marne - Paris 12 (UPEC UP12), Mathématiques financières (MATHFI), Laboratoire Jean Kuntzmann (LJK), Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS), LAMA-LJK, Centre National de la Recherche Scientifique (CNRS)-Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry]), and Centre National de la Recherche Scientifique (CNRS)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Université Joseph Fourier - Grenoble 1 (UJF)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Centre National de la Recherche Scientifique (CNRS)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Université Joseph Fourier - Grenoble 1 (UJF)-Université Pierre Mendès France - Grenoble 2 (UPMF)

Subjects
[MATH.MATH-PR]Mathematics [math]/Probability [math.PR], [QFIN.PR]Quantitative Finance [q-fin]/Pricing of Securities [q-fin.PR], parallel computing, backward stochastic differential equations, Monte-Carlo methods, non linear PDE, local volatility model, [INFO.INFO-DC]Computer Science [cs]/Distributed, Parallel, and Cluster Computing [cs.DC], American options, [QFIN.CP]Quantitative Finance [q-fin]/Computational Finance [q-fin.CP]
Abstract

25 pages; We present a parallel algorithm for solving backward stochastic differential equations (BSDEs in short) which are very useful theoretic tools to deal with many financial problems ranging from option pricing option to risk management. Our algorithm based on Gobet and Labart (2010) exploits the link between BSDEs and non linear partial differential equations (PDEs in short) and hence enables to solve high dimensional non linear PDEs. In this work, we apply it to the pricing and hedging of American options in high dimensional local volatility models, which remains very computationally demanding. We have tested our algorithm up to dimension 10 on a cluster of 512 CPUs and we obtained linear speedups which proves the scalability of our implementation

Published
2011

4. Solving BSDE with adaptive control variate. A note on the rate of convergence of the operator P^k

Author

Gobet, Emmanuel, Labart, Céline, Mathématiques financières (MATHFI), Laboratoire Jean Kuntzmann (LJK), Centre National de la Recherche Scientifique (CNRS)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Université Joseph Fourier - Grenoble 1 (UJF)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Centre National de la Recherche Scientifique (CNRS)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Université Joseph Fourier - Grenoble 1 (UJF)-Université Pierre Mendès France - Grenoble 2 (UPMF), Laboratoire de Probabilités et Modèles Aléatoires (LPMA), Centre National de la Recherche Scientifique (CNRS)-Université Paris Diderot - Paris 7 (UPD7)-Université Pierre et Marie Curie - Paris 6 (UPMC), Gobet, Emmanuel, Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS), and Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)

Subjects
[MATH.MATH-PR]Mathematics [math]/Probability [math.PR], [MATH.MATH-PR] Mathematics [math]/Probability [math.PR], [STAT.TH] Statistics [stat]/Statistics Theory [stat.TH], [STAT.TH]Statistics [stat]/Statistics Theory [stat.TH]
Abstract

This note is a complement of the paper "Solving BSDE with adaptive control variate". It deals with the convergence of the approximating operator P, based on a non parametric regression technique called local averaging. Although the computations are quite standard (see Hardle '92, Gyorfi etal. '02), the specificities of the paper are the following: - the support of the variables is unbounded; - the error has to be measured using specific L2-norms; - errors on the gradient are provided.

Published
2009

5. Donsker-Type Theorem for BSDEs: Rate of Convergence

Author

Christel Geiss, Céline Labart, Stefan Geiss, Philippe Briand, Labart, Céline, Laboratoire de Mathématiques (LAMA), Centre National de la Recherche Scientifique (CNRS)-Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry]), Department of Mathematics and Statistics [Jyväskylä Univ] (JYU), and University of Jyväskylä (JYU)

Subjects
Statistics and Probability, [MATH.MATH-PR] Mathematics [math]/Probability [math.PR], Markov process, Type (model theory), scaled random walk, 01 natural sciences, convergence rate, 010104 statistics & probability, symbols.namesake, Mathematics::Probability, Convergence (routing), FOS: Mathematics, Order (group theory), Applied mathematics, Wasserstein distance, 0101 mathematics, Donsker's theorem, stokastiset prosessit, Mathematics, konvergenssi, Probability (math.PR), 010102 general mathematics, Finite difference, Random walk, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], Rate of convergence, backward stochastic differential equations, symbols, approksimointi, Donsker’s theorem, finite difference scheme, differentiaaliyhtälöt, Mathematics - Probability
Abstract

In this paper, we study in the Markovian case the rate of convergence in Wasserstein distance when the solution to a BSDE is approximated by a solution to a BSDE driven by a scaled random walk as introduced in Briand, Delyon and Mémin (Electron. Commun. Probab. 6 (2001) Art. ID 1). This is related to the approximation of solutions to semilinear second order parabolic PDEs by solutions to their associated finite difference schemes and the speed of convergence. peerReviewed

Published
2019

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