Related papers: Multilevel Picard approximations for McKean-Vlasov…
In this work, in order to obtain higher-order schemes for solving forward backward stochastic differential equations, we adopt the high-order multi-step method in [W. Zhao, Y. Fu and T. Zhou, SIAM J. Sci. Comput., 36(4) (2014),…
We develop algorithms for computing expectations of the laws of models associated to stochastic differential equations (SDEs) driven by pure L\'evy processes. We consider filtering such processes and well as pricing of path dependent…
In this paper, we study multistage stochastic mixed-integer nonlinear programs (MS-MINLP). This general class of problems encompasses, as important special cases, multistage stochastic convex optimization with non-Lipschitzian value…
Backward stochastic differential equations (BSDEs) appear in numeruous applications. Classical approximation methods suffer from the curse of dimensionality and deep learning-based approximation methods are not known to converge to the BSDE…
We propose a new algorithm for solving multistage stochastic mixed integer linear programming (MILP) problems with complete continuous recourse. In a similar way to cutting plane methods, we construct nonlinear Lipschitz cuts to build lower…
Multi-stage stochastic linear programs (MSLPs) are notoriously hard to solve in general. Linear decision rules (LDRs) yield an approximation of an MSLP by restricting the decisions at each stage to be an affine function of the observed…
It is one of the most challenging problems in applied mathematics to approximatively solve high-dimensional partial differential equations (PDEs). Recently, several deep learning-based approximation algorithms for attacking this problem…
The work concerns a type of backward multivalued McKean-Vlasov stochastic differential equations. First, we prove the existence and uniqueness of solutions for backward multivalued McKean-Vlasov stochastic differential equations. Then, it…
The aim of this work is to provide fast and accurate approximation schemes for the Monte Carlo pricing of derivatives in LIBOR market models. Standard methods can be applied to solve the stochastic differential equations of the successive…
In this paper, we present a generic methodology for the efficient numerical approximation of the density function of the McKean-Vlasov SDEs. The weak error analysis for the projected process motivates us to combine the iterative Multilevel…
The work concerns deviation estimates for multivalued McKean-Vlasov stochastic differential equations. First of all, we prove the large deviation principle for them by the weak convergence approach. Then the central limit theorem for them…
Multilevel Monte Carlo (MLMC) has become an important methodology in applied mathematics for reducing the computational cost of weak approximations. For many problems, it is well-known that strong pairwise coupling of numerical solutions in…
In the stochastic gradient descent (SGD) for sequential simulations such as the neural stochastic differential equations, the Multilevel Monte Carlo (MLMC) method is known to offer better theoretical computational complexity compared to the…
This manuscript presents a framework for using multilevel quadrature formulae to compute the solution of optimal control problems constrained by random partial differential equations. Our approach consists in solving a sequence of optimal…
We propose and analyze deterministic multilevel approximations for Bayesian inversion of operator equations with uncertain distributed parameters, subject to additive Gaussian measurement data. The algorithms use a multilevel (ML) approach…
We propose several algorithms to solve McKean-Vlasov Forward Backward Stochastic Differential Equations. Our schemes rely on the approximating power of neural networks to estimate the solution or its gradient through minimization problems.…
We propose a new family of multilevel methods for unconstrained minimization. The resulting strategies are multilevel extensions of high-order optimization methods based on q-order Taylor models (with q >= 1) that have been recently…
In the following article we consider approximate Bayesian computation (ABC) inference. We introduce a method for numerically approximating ABC posteriors using the multilevel Monte Carlo (MLMC). A sequential Monte Carlo version of the…
Stochastic PDE eigenvalue problems are useful models for quantifying the uncertainty in several applications from the physical sciences and engineering, e.g., structural vibration analysis, the criticality of a nuclear reactor or photonic…
Cr\'epey, Frikha, and Louzi (2025) introduced a multilevel stochastic approximation scheme to compute the value-at-risk of a financial loss that is only simulatable by Monte Carlo. The best complexity of the scheme is in…