In this paper,we present a probabilistic numerical method for a class of forward utilities in a stochastic factor model.For this purpose,we use the representation of forward utilities using the ergodic Backward Stocha...In this paper,we present a probabilistic numerical method for a class of forward utilities in a stochastic factor model.For this purpose,we use the representation of forward utilities using the ergodic Backward Stochastic Differential Equations(eBSDEs)introduced by Liang and Zariphopoulou in[27].We establish a connection between the solution of the ergodic BSDE and the solution of an associated BSDE with random terminal time T,defined as the hitting time of the positive recurrent stochastic factor.The viewpoint based on BSDEs with random horizon yields a new characterization of the ergodic cost^which is a part of the solution of the eBSDEs.In particular,for a certain class of eBSDEs with quadratic generator,the Cole-Hopf transformation leads to a semi-explicit representation of the solution as well as a new expression of the ergodic cost>.The latter can be estimated with Monte Carlo methods.We also propose two new deep learning numerical schemes for eBSDEs.Finally,we present numerical results for different examples of eBSDEs and forward utilities together with the associated investment strategies.展开更多
This work deals with the numerical localization of small electromagnetic inhomogeneities. The underlying inverse problem considers, in a three-dimensional bounded domain, the time-harmonic Maxwell equations formulated...This work deals with the numerical localization of small electromagnetic inhomogeneities. The underlying inverse problem considers, in a three-dimensional bounded domain, the time-harmonic Maxwell equations formulated in electric field. Typically, the domain contains a finite number of unknown inhomogeneities of small volume and the inverse problem attempts to localize these inhomogeneities from a finite number of boundary measurements. Our localization approach is based on a recent framework that uses an asymptotic expansion for the perturbations in the tangential boundary trace of the curl of the electric field. We present three numerical localization procedures resulting from the combination of this asymptotic expansion with each of the following inversion algorithms： the Current Projection method, the MUltiple Signal Classification （MUSIC） algorithm, and an Inverse Fourier method. We perform a numerical study of the asymptotic expansion and compare the numerical results obtained from the three localization procedures in different settings.展开更多
The classical equations of a nonlinearly elastic plane membrane made of Saint Venant-Kirchhoff material have been justified by Fox, Raoult and Simo （1993） and Pantz （2000）. We show that, under compression, the ass...The classical equations of a nonlinearly elastic plane membrane made of Saint Venant-Kirchhoff material have been justified by Fox, Raoult and Simo （1993） and Pantz （2000）. We show that, under compression, the associated minimization problem admits no solution. The proof is based on a result of non-existence of minimizers of non-convex functionals due to Dacorogna and Marcellini （1995）. We generalize the application of their result from Diane elasticity to three-dimensional Diane membranes.展开更多
We introduce the Fast Free Memory method(FFM),a new implementation of the Fast Multipole Method(FMM)for the evaluation of convolution products.The FFM aims at being easier to implement while maintaining a high level o...We introduce the Fast Free Memory method(FFM),a new implementation of the Fast Multipole Method(FMM)for the evaluation of convolution products.The FFM aims at being easier to implement while maintaining a high level of performance,capable of handling industrially-sized problems.The FFM avoids the implementation of a recursive tree and is a kernel independent algorithm.We give the algorithm and the relevant complexity estimates.The quasi-linear complexity enables the evaluation of convolution products with up to one billion entries.We illustrate numerically the capacities of the FFM by solving Boundary Integral Equations problems featuring dozen of millions of unknowns.Our implementation is made freely available under the GPL 3.0 license within the Gypsilab framework.展开更多
We present a domain decomposition method （DDM） devoted to the iterative solution of time-harmonic electromagnetic scattering problems, involving large and resonant cavities. This DDM uses the electric field integral...We present a domain decomposition method （DDM） devoted to the iterative solution of time-harmonic electromagnetic scattering problems, involving large and resonant cavities. This DDM uses the electric field integral equation （EFIE） for the solution of Maxwell problems in both interior and exterior subdomains, and we propose a simple preconditioner for the global method, based on the single layer operator restricted to the fictitious interface between the two subdomains.展开更多
基金The authors research is part of the ANR project DREAMeS(ANR-21-CE46-0002)and benefited from the support of respectively the "Chair Risques Emergents en Assurance"and"Chair Impact de la Transition Climatique en Assurance"under the aegis of Fondation du Risque,a joint initiative by Risk and Insurance Institute of Le Mans,and MMA-Covea and Groupama respectively.
文摘In this paper,we present a probabilistic numerical method for a class of forward utilities in a stochastic factor model.For this purpose,we use the representation of forward utilities using the ergodic Backward Stochastic Differential Equations(eBSDEs)introduced by Liang and Zariphopoulou in[27].We establish a connection between the solution of the ergodic BSDE and the solution of an associated BSDE with random terminal time T,defined as the hitting time of the positive recurrent stochastic factor.The viewpoint based on BSDEs with random horizon yields a new characterization of the ergodic cost^which is a part of the solution of the eBSDEs.In particular,for a certain class of eBSDEs with quadratic generator,the Cole-Hopf transformation leads to a semi-explicit representation of the solution as well as a new expression of the ergodic cost>.The latter can be estimated with Monte Carlo methods.We also propose two new deep learning numerical schemes for eBSDEs.Finally,we present numerical results for different examples of eBSDEs and forward utilities together with the associated investment strategies.
基金supported by ACI NIM (171) from the French Ministry of Education and Scientific Research
文摘This work deals with the numerical localization of small electromagnetic inhomogeneities. The underlying inverse problem considers, in a three-dimensional bounded domain, the time-harmonic Maxwell equations formulated in electric field. Typically, the domain contains a finite number of unknown inhomogeneities of small volume and the inverse problem attempts to localize these inhomogeneities from a finite number of boundary measurements. Our localization approach is based on a recent framework that uses an asymptotic expansion for the perturbations in the tangential boundary trace of the curl of the electric field. We present three numerical localization procedures resulting from the combination of this asymptotic expansion with each of the following inversion algorithms： the Current Projection method, the MUltiple Signal Classification （MUSIC） algorithm, and an Inverse Fourier method. We perform a numerical study of the asymptotic expansion and compare the numerical results obtained from the three localization procedures in different settings.
文摘The classical equations of a nonlinearly elastic plane membrane made of Saint Venant-Kirchhoff material have been justified by Fox, Raoult and Simo （1993） and Pantz （2000）. We show that, under compression, the associated minimization problem admits no solution. The proof is based on a result of non-existence of minimizers of non-convex functionals due to Dacorogna and Marcellini （1995）. We generalize the application of their result from Diane elasticity to three-dimensional Diane membranes.
文摘We introduce the Fast Free Memory method(FFM),a new implementation of the Fast Multipole Method(FMM)for the evaluation of convolution products.The FFM aims at being easier to implement while maintaining a high level of performance,capable of handling industrially-sized problems.The FFM avoids the implementation of a recursive tree and is a kernel independent algorithm.We give the algorithm and the relevant complexity estimates.The quasi-linear complexity enables the evaluation of convolution products with up to one billion entries.We illustrate numerically the capacities of the FFM by solving Boundary Integral Equations problems featuring dozen of millions of unknowns.Our implementation is made freely available under the GPL 3.0 license within the Gypsilab framework.
文摘We present a domain decomposition method （DDM） devoted to the iterative solution of time-harmonic electromagnetic scattering problems, involving large and resonant cavities. This DDM uses the electric field integral equation （EFIE） for the solution of Maxwell problems in both interior and exterior subdomains, and we propose a simple preconditioner for the global method, based on the single layer operator restricted to the fictitious interface between the two subdomains.
