COMPLETE SPECIFICATION OF SOME PARTIAL DIFFERENTIAL EQUATIONS THAT ARISE IN FINANCIAL MATHEMATICS

被引：18

作者：

Dimas, S. ^{[1
]}

Andriopoulos, K. ^{[1
,2
,3
]}

Tsoubelis, D. ^{[1
]}

Leach, P. G. L. ^{[1
,2
]}

机构：

[1] Univ Patras, Dept Math, Patras 26500, Greece

[2] Univ KwaZulu Natal, Sch Math Sci, ZA-4000 Durban, South Africa

[3] Ctr Res & Applicat Nonlinear Syst, Patras, Greece

来源：

JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS | 2009年 / 16卷

关键词：

Modern group analysis; Financial Mathematics; Lie remarkability; Black-Scholes equation; Cox-Ingersoll-Ross equation;

D O I：

10.1142/S1402925109000339

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider some well-known partial differential equations that arise in Financial Mathematics, namely the Black-Scholes-Merton, Longstaff, Vasicek, Cox-Ingersoll-Ross and Heath equations. Our central aim is to discover any underlying connections taking into account the Lie remarkability property of the heat equation. For a few of these equations there is a known connection with the heat equation through a coordinate transformation. We investigate further that connection with the help of modern group analysis. This is realized by obtaining the Lie point symmetries of these equations and comparing their algebras with that of the heat equation. For those with an algebra identical to that of the heat equation a systematic way is shown to obtain the coordinate transformation that links them: the Lie remarkability property is a direct consequence. For the rest this is achieved only in certain subcases.

引用

页码：73 / 92

页数：20

共 30 条

[1]

Andriopoulos K, 2006, S AFR J SCI, V102, P66

[2] On the systematic approach to the classification of differential equations by group theoretical methods [J].