Using Chebyshev Polynomials to Approximate Partial Differential Equations

被引：11

作者：

Caporale, Guglielmo Maria ^{[1
]}

Cerrato, Mario ^{[2
]}

机构：

[1] Brunel Univ, Ctr Empir Finance, Uxbridge UB8 3PH, Middx, England

[2] Univ Glasgow, Dept Econ, Glasgow, Lanark, Scotland

来源：

COMPUTATIONAL ECONOMICS | 2010年 / 35卷 / 03期

关键词：

European options; Chebyshev polynomial approximation; Chebyshev nodes; INVESTMENT; OPTIONS;

D O I：

10.1007/s10614-009-9172-8

中图分类号：

F [经济];

学科分类号：

02 ;

摘要：

This paper suggests a simple method based on a Chebyshev approximation at Chebyshev nodes to approximate partial differential equations (PDEs). It consists in determining the value function by using a set of nodes and basis functions. We provide two examples: pricing a European option and determining the best policy for shutting down a machine. The suggested method is flexible, easy to programme and efficient. It is also applicable in other fields, providing efficient solutions to complex systems of PDEs.

引用

页码：235 / 244

页数：10

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