Electronic Journal of Differential Equations,
Vol. 2011 (2011), No. 158, pp. 1-10.

Title: Solution to a nonlinear Black-Scholes equation

Authors: Maria Cristina Mariani (The Univ. of Texas at El Paso, TX, USA)
         Emmanuel K.  Ncheuguim (New Mexico State Univ., Las Cruces, NM, USA)
	 Indranil SenGupta  (The Univ. of Texas at El Paso, TX, USA)

Abstract:
 Option pricing with transaction costs leads to a nonlinear
 Black-Scholes type equation where the nonlinear term reflects
 the presence of transaction costs. Under suitable conditions,
 we prove the existence of weak solutions in a bounded domain
 and we extend the results to the whole domain using a diagonal
 process.

Submitted August 20, 2010. Published November 28, 2011.
Math Subject Classifications: 91G80, 35B45, 58J35, 35D30.
Key Words: Option pricing; Black-Scholes equation; Sobolev space;
           Schaefer's fixed point theorem.