Browsing by Author "Leach, Peter G. L."
Now showing items 1-12 of 12
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Algebraic aspects of evolution partial differential equations arising in financial mathematics
Sophocleous, Christodoulos; Leach, Peter G. L. (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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Algebraic properties of evolution partial differential equations modelling prices of commodities
Sophocleous, Christodoulos; Leach, Peter G. L.; Andriopoulos, Konstantinos (2008)Schwartz (J. Finance 1997
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Algebraic solution of the Stein-Stein model for stochastic volatility
Sophocleous, Christodoulos; O'Hara, John G.; Leach, Peter G. L. (2011)We provide an algebraic approach to the solution of the Stein-Stein model for stochastic volatility which arises in the determination of the Radon-Nikodym density of the minimal entropy of the martingale measure. We extend ...
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Application of Lie point symmetries to the resolution of certain problems in financial mathematics with a terminal condition
O'Hara, John G.; Sophocleous, Christodoulos; Leach, Peter G. L. (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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A deductive approach to the solution of the problem of optimal pairs trading from the viewpoint of stochastic control with time-dependent parameters
Charalambous, Kyriakos; Sophocleous, Christodoulos; O'Hara, John G.; Leach, Peter G. L. (2015)In a fairly recent paper (2008 American Control Conference, June 11-13, 1035-1039), the problem of dealing with trading in optimal pairs was treated from the viewpoint of stochastic control. The analysis of the subsequent ...
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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]
O’Hara, J. G.; Sophocleous, Christodoulos; Leach, Peter G. L. (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
Ivanova, Nataliya M.; Sophocleous, Christodoulos; Leach, Peter G. L. (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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Lie symmetries of generalized Burgers equations: application to boundary-value problems
Vaneeva, Olena O.; Sophocleous, Christodoulos; Leach, Peter G. L. (2015)There exist several approaches exploiting Lie symmetries in the reduction of boundary-value problems for partial differential equations modelling real-world phenomena to those problems for ordinary differential equations. ...
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Symmetry analysis of a model for the exercise of a barrier option
O'Hara, John G.; Sophocleous, Christodoulos; Leach, Peter G. L. (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 analysis of a model of stochastic volatility with time-dependent parameters
Sophocleous, Christodoulos; O'Hara, John G.; Leach, Peter G. L. (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
Charalambous, Kyriakos; Sophocleous, Christodoulos; Leach, Peter G. L. (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
Sophocleous, Christodoulos; Leach, Peter G. L. (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 ...