Journal of Nonlinear Mathematical Physics

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Volume 16, Issue Supplement 1, December 2009, Pages 73 - 92

Complete Specification of Some Partial Differential Equations That Arise in Financial Mathematics

Authors
S. Dimas*, §, K. Andriopoulos*, †, ‡, , D. Tsoubelis*, ‖, P. G. L. Leach*, †, **
*Department of Mathematics, University of Patras, 26500 Patras, Greece
†School of Mathematical Sciences, University of KwaZulu-Natal, Private Bag X54001, Durban 4000, Republic of South Africa
‡Centre for Research and Applications of Nonlinear Systems, Patras, Greece
Received 28 August 2009, Accepted 21 September 2009, Available Online 7 January 2021.
DOI
10.1142/S1402925109000339How to use a DOI?
Keywords
Modern group analysis; Financial Mathematics; Lie remarkability; Black–Scholes equation; Cox–Ingersoll–Ross equation
Abstract

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.

Copyright
© 2009 The Authors. Published by Atlantis Press and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
16 - Supplement 1
Pages
73 - 92
Publication Date
2021/01/07
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.1142/S1402925109000339How to use a DOI?
Copyright
© 2009 The Authors. Published by Atlantis Press and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

risenwbib
TY  - JOUR
AU  - S. Dimas
AU  - K. Andriopoulos
AU  - D. Tsoubelis
AU  - P. G. L. Leach
PY  - 2021
DA  - 2021/01/07
TI  - Complete Specification of Some Partial Differential Equations That Arise in Financial Mathematics
JO  - Journal of Nonlinear Mathematical Physics
SP  - 73
EP  - 92
VL  - 16
IS  - Supplement 1
SN  - 1776-0852
UR  - https://doi.org/10.1142/S1402925109000339
DO  - 10.1142/S1402925109000339
ID  - Dimas2021
ER  -