Recently the liquidity of financial markets and transaction costs have become a topic of great interest in financial risk management. In this paper, a hypotetical nonlinear model of option pricing that occurs when the effects of market illiquidity and transaction costs are taken into account and an approximate solution is obtained through the Adomian decomposition method. Finally, two numerical examples are investigated to demonstrate the efficiency of our approach.

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The recently proposed approximate nonconformal (ANC) theory has been very successful in determining effective interaction potentials for a large number of pure substances in the gaseous state: noble gases, homodiatomics, alkanes, perfluoroalkanes and some small polyatomic molecules, as well as many of their binary mixtures. ANC potentials are spherically symmetric Kihara-like functions involving an energy ", a diameter and a form parameter s. In this work, we propose an effective-potential theory valid at finite densities. The basic assumption is that ANC potential functions represent effectively the thermodynamics of a substance over the isotropic fluid region given the appropriate state dependencies of ", and s. The theory proposes a relation between the critical temperature of a substance and " that is used here to predict effective potentials for the one-carbon Freons: CCl a collection of small molecules that are all of similar geometry but varying degrees of polarity. As a test of the reliability of the theory the calculated second virial coefficients B(T ) are compared with experiment. For most of these substances, B(T ) is reproduced within experimental error. The relative contributions of the polar and nonpolar parts of the potential to the thermodynamics are discussed. The approach produces effective interactions and generalized Stockmayer potentials for this set of molecules to be used in predicting other thermodynamic properties.