Browsing by Subject "Lie point symmetries"
Now showing items 1-5 of 5
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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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Symmetry analysis of a model of stochastic volatility with time-dependent parameters
(2011)We provide the solutions for the Heston model of stochastic volatility when the parameters of the model are constant and when they are functions of time. In the former case, the solution follows immediately from the ...
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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 ...