Non-linear Modifications of Black-Scholes Pricing Model with Diminishing Marginal Transaction Cost

In the field of quantitative financial analysis, the Black-Scholes Model has exerted significant influence on the booming of options trading strategies. Publishing in their Nobel Prize Work in 1973, the model was generated by Black and Scholes. Using Ito’s Lemma and portfolio management methodology, they employed partial differential equation to provide a theoretical estimate of the price of European-style options. This paper is interested in deriving non-linear modifications of the Black-Scholes model with diminishing marginal transaction cost