I am working on a project related to Nonlinear BS partial differential equation, with terms for transaction costs and/or discrete hedging. I have two questions:
Is there any exact solution to the Nonlinear BS equation?
I have read a paper which numerically solved a Nonlinear BS and compared results with Linear BS. Nonlinear BS is supposed to be giving different option price than Linear one. Why should we compare them ? the paper
Lastly, as I am working on a project , it will be extremely helpful if you can provide some references that backs your statements.