2013/09/15 by José Arturo Infante Acevedo, Tony Lelièvre, Acevedo, José Arturo Infante +1
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Approximation and Integration #Numerical Analysis (math.NA) #Probabilistic and Robust Engineering Design #Stochastic processes and financial applications
paper · doi:10.48550/arxiv.1309.3731
openalex publication_date 2013/09/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study an algorithm which has been proposed by Chinesta et al. to solve high-dimensional partial differential equations. The idea is to represent the solution as a sum of tensor products and to compute iteratively the terms of this sum. This algorithm is related to the so-called greedy algorithm introduced by Temlyakov. In this paper, we investigate the application of the greedy algorithm in finance and more precisely to the option pricing problem. We approximate the solution to the Black-Scholes equation and we propose a variance reduction method. In numerical experiments, we obtain results for up to 10 underlyings. Besides, the proposed variance reduction method permits an important reduction of the variance in comparison with a classical Monte Carlo method.