کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
5127980 1489371 2018 21 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
A non linear approximation method for solving high dimensional partial differential equations: Application in finance
ترجمه فارسی عنوان
یک روش تقریبی غیر خطی برای حل معادلات دیفرانسیل با مقدار بعدی: کاربرد در امور مالی
موضوعات مرتبط
مهندسی و علوم پایه سایر رشته های مهندسی کنترل و سیستم های مهندسی
چکیده انگلیسی

We study an algorithm which has been proposed by A. Ammar, B. Mokdad, F. Chinesta, R. Keunings in 2006 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 algorithms, as introduced by V.N. 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.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Mathematics and Computers in Simulation - Volume 143, January 2018, Pages 14-34
نویسندگان
, ,