Paper Info
Title
A non linear approximation method for solving high dimensional partial differential equations: Application in Finance
Abstract
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.
Year
Venue
Field
2018
Mathematics and Computers in Simulation
Tensor product,Mathematical optimization,Monte Carlo method,Valuation of options,Greedy algorithm,Non linear approximation,Finance,Variance reduction,Partial differential equation,Mathematics
DocType
Volume
Citations 
Journal
143
0
PageRank 
References 
Authors
0.34
0
2
Name
Order
Citations
PageRank
jose arturo infante acevedo100.34
Tony Lelièvre2339.48