- - - Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran
- - - Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran

The nonlinear Black-Scholes equation has been increasingly attracting interest over the last two decades, because it provides more accurate values by considering transaction costs as a viable assumption. In this paper we review the fully nonlinear Black-Scholes equation with an adjusted volatility which is a function of the second derivative of the price and then we prove two new theorems in this realistic model.

Nonlinear Black-Scholes equation, Transaction costs, Utility function