5 papers
Quasi-Monte Carlo finite element approximation for singularly perturbed convection-diffusion problems with random velocity
Seungchan Ko, Guanglian Li, Yi Yu
This paper studies the numerical approximation of a singularly perturbed convection-diffusion problem over a bounded polygonal domain in (), where the velocit…
Dual Variational Neural Network for the -Laplace Problem
Tianhao Hu, Guanglian Li, Fengru Wang +2
The reliable and accurate numerical approximation of the -Laplacian is particularly challenging in the extreme regimes and , where the operator becomes ei…
A deep primal-dual BSDE method for optimal stopping problems
Jiefei Yang, Guanglian Li
We present a new deep primal-dual backward stochastic differential equation framework based on stopping time iteration to solve optimal stopping problems. A novel loss function is…
Gradient-enhanced sparse Hermite polynomial expansions for pricing and hedging high-dimensional American options
Jiefei Yang, Guanglian Li
We propose an efficient and easy-to-implement gradient-enhanced least squares Monte Carlo method for computing price and Greeks (i.e., derivatives of the price function) of high-di…
On Sparse Grid Interpolation for American Option Pricing with Multiple Underlying Assets
Jiefei Yang, Guanglian Li
In this work, we develop a novel efficient quadrature and sparse grid based polynomial interpolation method to price American options with multiple underlying assets. The approach…