Browsing by Author "Sophocleous, Christodoulos"
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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

Article
Algebraic solution of the SteinStein 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 SteinStein model for stochastic volatility which arises in the determination of the RadonNikodym density of the minimal entropy of the martingale measure. We extend ...

Article
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 ...

Article
Bäcklund transformations for generalized nonlinear Schrödinger equations
Kingston, John G.; Sophocleous, Christodoulos (1990)A general class of Bäcklund transformations are considered for equations of the form izy + zxx + f(z,z̄) = 0, where f(z,z̄) is a function of z = x + iy and z̄ = x  iy. The nonlinear forms of this equation that admit such ...

Article
A class of Bäcklund transformations for equations of the type u xy=f(u,ux)
Sophocleous, Christodoulos; Kingston, John G. (1991)The Bäcklund transformation u = F(u′,u′x, u′y) is considered for equations of the form uxy = f(u,ux). The nonlinear forms of f(u,ux) that admit such transformations are completely classified. New Bäcklund transformations ...

Article
Classification of noether symmetries for Lagrangians with three degrees of freedom
Damianou, Pantelis A.; Sophocleous, Christodoulos (2004)The noether symmetries of the EulerLagrange equations for a Hamiltonian system with three degrees were classified. All groups were classified that appeared as symmetries of a general Hamiltonians system of n degrees of ...

Article
Classification of potential symmetries of generalised inhomogeneous nonlinear diffusion equations
Sophocleous, Christodoulos (2003)We consider the class of generalised nonlinear diffusion equations f(x)ut = [g(x)unux]x which are of considerable interest in mathematical physics. We classify the nonlocal symmetries, which are known as potential symmetries, ...

Article
Classification of reduction operators and exact solutions of variable coefficient Newell–Whitehead–Segel equations
Vaneeva, Olena; Boyko, Vyacheslav; Zhalij, Alexander; Sophocleous, Christodoulos (2019)A class of the Newell–Whitehead–Segel equations (also known as generalized Fisher equations and Newell–Whitehead equations) is studied with Lie and “nonclassical” symmetry points of view. The classifications of Lie reduction ...

Article
Conservation laws and hierarchies of potential symmetries for certain diffusion equations
Ivanova, Nataliya M.; Popovych, R. O.; Sophocleous, Christodoulos; Vaneeva, Olena O. (2009)We show that the socalled hidden potential symmetries considered in a recent paper [M.L. Gandarias, New potential symmetries for some evolution equations, Physica A 387 (2008) 22342242] are ordinary potential symmetries ...

Article
Conservation laws and potential symmetries of systems of diffusion equations
Ivanova, Nataliya M.; Sophocleous, Christodoulos (2008)We classify local firstorder conservation laws for a class of systems of nonlinear diffusion equations. The derived conservation laws are used to construct the set of inequivalent potential systems for the class under ...

Article
Continuous and discrete transformations of a onedimensional porous medium equation
Sophocleous, Christodoulos (1999)We consider the onedimensional porous medium equation (Formula presented.) We derive point transformations of a general class that map this equation into itself or into equations of a similar class. In some cases this ...

Article
Cyclic symmetries of onedimensional nonlinear wave equations
Sophocleous, Christodoulos; Kingston, John G. (1998)Symmetries corresponding to point transformations of four common classes of onedimensional nonlinear wave equations: utt = [F(u)ux]x

Article
A deductive approach to the solution of the problem of optimal pairs trading from the viewpoint of stochastic control with timedependent parameters
Charalambous, Kyriakos; Sophocleous, Christodoulos; O'Hara, John G.; Leach, Peter G. L. (2015)In a fairly recent paper (2008 American Control Conference, June 1113, 10351039), the problem of dealing with trading in optimal pairs was treated from the viewpoint of stochastic control. The analysis of the subsequent ...

Article
Differential invariants for quasilinear and semilinear wavetype equations
Sophocleous, Christodoulos; Tracinà, Rita (2008)In this paper, we consider the class of wavetype equations utt = f (x, t, u) uxx + g (x, t, u, ux, ut) and two special cases of it. We derive the equivalence transformations for these equations and using these transformations, ...

Article
Differential invariants for systems of linear hyperbolic equations
Tsaousi, Christina; Sophocleous, Christodoulos (2010)In this paper we consider a general class of systems of two linear hyperbolic equations. Motivated by the existence of the Laplace invariants for the single linear hyperbolic equation, we adopt the problem of finding ...

Article
Differential invariants for thirdorder evolution equations
Tsaousi, Christina; Tracinà, Rita; Sophocleous, Christodoulos (2015)We consider a general class of third order evolution equations. We construct differential invariants with the employment of the infinitesimal method that using equivalence groups. We use the differential invariants to ...

Article
Differential invariants of the onedimensional quasilinear secondorder evolution equation
Ibragimov, Nail Kh; Sophocleous, Christodoulos (2007)We consider evolution equations of the form ut = f(x, u, ux)uxx + g(x, u, ux) and ut = uxx + g(x, u, ux). In the spirit of the recent work of Ibragimov [Ibragimov NH. Laplace type invariants for parabolic equations. Nonlinear ...

Article
Enhanced group analysis and conservation laws of variable coefficient reactiondiffusion equations with power nonlinearities
Vaneeva, Olena O.; Johnpillai, A. G.; Popovych, R. O.; Sophocleous, Christodoulos (2007)A class of variable coefficient (1 + 1)dimensional nonlinear reactiondiffusion equations of the general form f (x) ut = (g (x) un ux)x + h (x) um is investigated. Different kinds of equivalence groups are constructed ...

Article
Enhanced group analysis and exact solutions of variable coefficient semilinear diffusion equations with a power source
Vaneeva, Olena O.; Popovych, R. O.; Sophocleous, Christodoulos (2009)A new approach to group classification problems and more general investigations on transformational properties of classes of differential equations is proposed. It is based on mappings between classes of differential ...