The Lie symmetry approach on (1+2)-dimensional financial models

K. Charalambous (), S. Kontogiorgis () and C. Sophocleous ()
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K. Charalambous: University of Cyprus
S. Kontogiorgis: University of Cyprus
C. Sophocleous: University of Cyprus

Partial Differential Equations and Applications, 2021, vol. 2, issue 4, 1-17

Abstract: Abstract We consider a class of nonlinear (1+2) partial differential equations which generalizes a number of models which appear in financial mathematics. These models are subject to specific terminal conditions. Lie symmetries are used to construct two successive mappings that reduce the problems into problems with new governing equations being ordinary differential equations. The same analysis is applied to general terminal conditions. In most cases, the first reduction results to linearizable equations. We discuss linearization for a general class which includes these reduced equations.

Keywords: Financial models; Lie symmetries; Similarity reductions; Problems with terminal condition; Linearization; 35A30; 35K55; 58J70 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s42985-021-00112-9

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