Browsing by Subject "Evolution partial differential equations"
Now showing items 1-7 of 7
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Algebraic aspects of evolution partial differential equations arising in financial mathematics
(2010)In the modelling of various financial instruments, risks, prices of commodities, etc., the end result is frequently an evolution partial differential equation. A remarkable number of these have rich algebraic structures. ...
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Application of Lie point symmetries to the resolution of certain problems in financial mathematics with a terminal condition
(2013)We demonstrate the power of symmetry in the resolution of some evolution partial differential equations which arise in various aspects of finance. The essential theme is that which Lie promulgated approximately 140 years ...
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Erratum: The application of Lie point symmetries to the resolution of certain problems in financial mathematics with a terminal condition [J Eng Math, 82, (2013), 67-75, DOI 10.1007/s10665-012-9595-4]
(2015)In an analysis of the Lie point symmetries of the equation which allows for the inclusion of transaction costs into the Black–Scholes model (J Eng Math 82:67–75, 2013) one of the symmetries was omitted. We rectify that ...
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Group classification of a class of equations arising in financial mathematics
(2010)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 ...
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Symmetry analysis of a model for the exercise of a barrier option
(2013)A barrier option takes into account the possibility of an unacceptable change in the price of the underlying stock. Such a change could carry considerable financial loss. We examine one model based upon the Black-Scholes-Merton ...
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Symmetry and singularity analyses of some equations of the fifth and sixth order in the spatial variable arising from the modelling of thin films
(2013)In the modelling of the flow of thin films higher-order derivatives in the spatial variable are introduced to model nonlinear effects. We examine nonlinear evolution equations of the fifth and sixth orders in the spatial ...
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Thin films: Increasing the complexity of the model
(2012)Thin films arise in a variety of contexts. They can be between two solid surfaces in the form of a lubricant or with one surface solid and the other free as in water or oil on a road. When the surface tension is a dominant ...