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Your search keyword '"Labart, Céline"' showing total 5 results
Start Over Author "Labart, Céline" Topic backward stochastic differential equations
5 results on '"Labart, Céline"'

1. Mean square rate of convergence for random walk approximation of forward-backward SDEs.

Author

Geiss, Christel, Labart, Céline, and Luoto, Antti

Abstract

Let (Y, Z) denote the solution to a forward-backward stochastic differential equation (FBSDE). If one constructs a random walk $B^n$ from the underlying Brownian motion B by Skorokhod embedding, one can show $L_2$ -convergence of the corresponding solutions $(Y^n,Z^n)$ to $(Y, Z).$ We estimate the rate of convergence based on smoothness properties, especially for a terminal condition function in $C^{2,\alpha}$. The proof relies on an approximative representation of $Z^n$ and uses the concept of discretized Malliavin calculus. Moreover, we use growth and smoothness properties of the partial differential equation associated to the FBSDE, as well as of the finite difference equations associated to the approximating stochastic equations. We derive these properties by probabilistic methods. [ABSTRACT FROM AUTHOR]

Published
2020
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2. 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

3. A parallel algorithm for solving BSDEs.

Author

Labart, Céline and Lelong, Jérôme

Subjects
*PARALLEL algorithms, *MONTE Carlo method, *STOCHASTIC differential equations, *ITERATIVE methods (Mathematics), *NONLINEAR theories, *HIGH performance computing
Abstract

We present a parallel algorithm for solving backward stochastic differential equations. We improve the algorithm proposed by Gobet and Labart (2010) based on an adaptive Monte Carlo method with Picard's iterations, and propose a parallel version of it. We test our algorithm on linear and nonlinear drivers up to dimension 8 on a cluster of 312 CPUs. We obtained very encouraging efficiency ratios greater than 0.7. [ABSTRACT FROM AUTHOR]

Published
2013
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4. SOLVING BSDE WITH ADAPTIVE CONTROL VARIATE.

Author

Gobet, Emmanuel and Labart, Céline

Subjects
*ALGORITHMS, *VARIATE difference method, *STOCHASTIC convergence, *PICARD schemes, *STOCHASTIC differential equations, *MONTE Carlo method
Abstract

We present and analyze an algorithm to solve numerically BSDEs based on Picard's iterations and on a sequential control variate technique. Its convergence is geometric. Moreover, the solution provided by our algorithm is regular both w.r.t. time and space. [ABSTRACT FROM AUTHOR]

Published
2010
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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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