<p>We consider one transaction costs model which was suggested by Cetin, Jarrow and Protter (2004) for an illiquid market. In this case the hedging strategy of programming traders can affect the assets prises. We study the corresponding partial differential equation (PDE) which is a non-linear Black-Scholes equation for illiquid markets. We use the Lie group analysis to determine the symmetry group of this equations. We present the Lie algebra of the Lie point transformations, the complete symmetry group and invariants. For different subgroups of the main symmetry group we describe the corresponding invariants. We use these invariants to reduce the PDE under investigation to ordinary differential equations (ODE). Solutions of these ODE's are subgroup-invariant solutions of the non-linear Black-Scholes equation. For some classes of those ODE's we find exact solutions and studied their properties.</p><p>% reduce non-linear PDE to ODE's. To some ODE's we find exact solutions.</p><p>%In this work we are studying one model for pricing derivatives in illiquid market. We discuss it structure and properties. Make a symmetry reduction for the PDE corresponding our model.</p>

We consider one transaction costs model which was suggested by Cetin, Jarrow and Protter (2004) for an illiquid market. In this case the hedging strategy of programming traders can affect the assets prises. We study the corresponding partial differential equation (PDE) which is a non-linear Black-Scholes equation for illiquid markets. We use the Lie group analysis to determine the symmetry group of this equations. We present the Lie algebra of the Lie point transformations, the complete symmetry group and invariants. For different subgroups of the main symmetry group we describe the corresponding invariants. We use these invariants to reduce the PDE under investigation to ordinary differential equations (ODE). Solutions of these ODE's are subgroup-invariant solutions of the non-linear Black-Scholes equation. For some classes of those ODE's we find exact solutions and studied their properties. % reduce non-linear PDE to ODE's. To some ODE's we find exact solutions. %In this work we are studying one model for pricing derivatives in illiquid market. We discuss it structure and properties. Make a symmetry reduction for the PDE corresponding our model.

<p>The master thesis is devoted to an analysis of equilibrium or reaction-function models in illiquidity markets of derivatives. The main equation is a nonlinear equation which is a perturbation of Black-Scholes model. By using analytical methods we study invariant and scaling properties for the considered model.</p>

The master thesis is devoted to an analysis of equilibrium or reaction-function models in illiquidity markets of derivatives. The main equation is a nonlinear equation which is a perturbation of Black-Scholes model. By using analytical methods we study invariant and scaling properties for the considered model.

<p>In this paper it is considered the Sircar-Papanicolaou model wich takesinto account a feedback effect of dynamic hedging strategies of pro-gramme traders. Using the Lie group analysis we describe the symmetrygroup of the main equation of the concerned model. We reduce this par-tial differential equation to the ordinary differential equations by usingcorresponding invariants of the subgroups of the main symmetry group.</p>

In this paper it is considered the Sircar-Papanicolaou model wich takesinto account a feedback effect of dynamic hedging strategies of pro-gramme traders. Using the Lie group analysis we describe the symmetrygroup of the main equation of the concerned model. We reduce this par-tial differential equation to the ordinary differential equations by usingcorresponding invariants of the subgroups of the main symmetry group.

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<p>This master project is dedicated to the analysis of one of the nancialmarket models in an illiquid market. This is a nonlinear model. Using analytical methods we studied the symmetry properties of theequation which described the given model. We called this equation aSchonbucher-Wilmott equation or the main equation. We have foundinnitesimal generators of the Lie algebra, containing the informationabout the symmetry group admitted by the main equation. We foundthat there could be dierent types of the unknown function g, whichwas located in the main equation, in particular four types which admitsricher symmetry group. According to the type of the function gthe equation was split up into four PDEs with the dierent Lie algebrasin each case. Using the generators we studied the structure ofthe Lie algebras and found optimal systems of subalgebras. Then weused the optimal systems for dierent reductions of the PDE equationsto some ODEs. Obtained ODEs were easier to solve than the correspondingPDE. Thereafter we proceeded to the solution of the desiredSchonbucher-Wilmott equation. In the project we were guided by thepapers of Bank, Baum [1] and Schonbucher, Wilmott [2]. In these twopapers authors introduced distinct approaches of the analysis of thenonlinear model - stochastic and dierential ones. Both approaches leadunder some additional assumptions to the same nonlinear equation - the main equation.</p>

This master project is dedicated to the analysis of one of the nancialmarket models in an illiquid market. This is a nonlinear model. Using analytical methods we studied the symmetry properties of theequation which described the given model. We called this equation aSchonbucher-Wilmott equation or the main equation. We have foundinnitesimal generators of the Lie algebra, containing the informationabout the symmetry group admitted by the main equation. We foundthat there could be dierent types of the unknown function g, whichwas located in the main equation, in particular four types which admitsricher symmetry group. According to the type of the function gthe equation was split up into four PDEs with the dierent Lie algebrasin each case. Using the generators we studied the structure ofthe Lie algebras and found optimal systems of subalgebras. Then weused the optimal systems for dierent reductions of the PDE equationsto some ODEs. Obtained ODEs were easier to solve than the correspondingPDE. Thereafter we proceeded to the solution of the desiredSchonbucher-Wilmott equation. In the project we were guided by thepapers of Bank, Baum [1] and Schonbucher, Wilmott [2]. In these twopapers authors introduced distinct approaches of the analysis of thenonlinear model - stochastic and dierential ones. Both approaches leadunder some additional assumptions to the same nonlinear equation - the main equation.