Properties of utility function for Barles and Soner model

Document Type : Research Paper


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.


Volume 7, Issue 1
January 2019
Pages 117-123
  • Receive Date: 30 December 2017
  • Revise Date: 29 May 2018
  • Accept Date: 26 November 2018
  • First Publish Date: 01 January 2019