Group classification of a class of equations arising in financial mathematics

被引：4

作者：

Ivanova, N. M. ^{[1
,2
]}

Sophocleous, C. ^{[1
]}

Leach, P. G. L. ^{[1
,3
]}

机构：

[1] Univ Cyprus, Dept Math & Stat, CY-1678 Nicosia, Cyprus

[2] Natl Acad Sci Ukraine, Inst Math, UA-01601 Kiev, Ukraine

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

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2010年 / 372卷 / 01期

关键词：

Group classification; Financial mathematics; Evolution partial differential equations; STOCHASTIC VOLATILITY; SYMMETRIES; OPTIONS;

D O I：

10.1016/j.jmaa.2010.06.018

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We provide a group classification of a class of nonlinearisable evolution partial differential equations which arise in Financial Mathematics. Sixteen different cases are identified for the general problem and another seven for a restricted version. In the cases for which the algebra is suitable we determine the solution to the problem u(0, x) = U, where U is a constant. In addition we provide a number of solutions based upon reduction using inequivalent subalgebras. (C) 2010 Elsevier Inc. All rights reserved.

引用

页码：273 / 286

页数：14

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