University of Tabriz Computational Methods for Differential Equations 2345-3982 7 1 2019 01 01 Properties of utility function for Barles and Soner model 117 123 8178 EN Mojtaba Ranjbar Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran Somayeh Pourghanbar Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran Journal Article 2017 12 30 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. https://cmde.tabrizu.ac.ir/article_8178_eb961039a8ddf83ca42eeee832a76ae9.pdf