113 citations · 1k across the 84 of their papers we have counts for
8 papers · 1 filter
Deep NURBS -- Admissible Physics-informed Neural Networks
Hamed Saidaoui, Luis Espath, Rául Tempone
In this study, we propose a new numerical scheme for physics-informed neural networks (PINNs) that enables precise and inexpensive solution for partial differential equations (PDEs…
Multilevel Importance Sampling for Rare Events Associated With the McKean--Vlasov Equation
Nadhir Ben Rached, Abdul-Lateef Haji-Ali, Shyam Mohan Subbiah Pillai +1
This work combines multilevel Monte Carlo (MLMC) with importance sampling to estimate rare-event quantities that can be expressed as the expectation of a Lipschitz observable of th…
Approximating Hessian matrices using Bayesian inference: a new approach for quasi-Newton methods in stochastic optimization
Andre Carlon, Luis Espath, Raul Tempone
Using quasi-Newton methods in stochastic optimization is not a trivial task given the difficulty of extracting curvature information from the noisy gradients. Moreover, pre-conditi…
Double-Loop Importance Sampling for McKean--Vlasov Stochastic Differential Equation
Nadhir Ben Rached, Abdul-Lateef Haji-Ali, Shyam Mohan Subbiah Pillai +1
This paper investigates Monte Carlo (MC) methods to estimate probabilities of rare events associated with solutions to the -dimensional McKean-Vlasov stochastic differential equ…
Goal-Oriented Adaptive Finite Element Multilevel Monte Carlo with Convergence Rates
Joakim Beck, Yang Liu, Erik von Schwerin +1
We present an adaptive multilevel Monte Carlo (AMLMC) algorithm for approximating deterministic, real-valued, bounded linear functionals that depend on the solution of a linear ell…
Optimal Damping with Hierarchical Adaptive Quadrature for Efficient Fourier Pricing of Multi-Asset Options in Lévy Models
Michael Samet, Christian Bayer, Chiheb Ben Hammouda +2
Efficiently pricing multi-asset options is a challenging problem in quantitative finance. When the characteristic function is available, Fourier-based methods are competitive compa…