On a nonlinear transaction-cost model for stock prices in an illiquid market driven by a relaxed black-scholes model assumptions

In an illiquid market,assets cannot be easily sold or exchanged for cash without a loss of value (even if it is minimal),this may be due to uncertainty such as transaction cost,lack of interested buyers and so on. this paper considers a nonlinear transaction-cost model for stock prices in an illiquid market. this nonlinear model surfaced when the constant volatility assumption of the famous linear black-scholes option valuation and pricing model is relaxed via the inclusion of transaction cost. we obtain approximate solutions to this nonlinear model using the projected differential transform technique or method (pdtm) as a semi-analytical method. the results are very interesting,agree with the associated exact solutions of esekon (2013) and that of gonzalez-gaxiola et al. (2015).