Solutions to a stationary nonlinear Black–Scholes type equation

We study by topological methods a nonlinear differential equation generalizing the Black–Scholes formula for an option pricing model with stochastic volatility. We prove the existence of at least a solution of the stationary Dirichlet problem applying an upper and lower solutions method. Moreover, we construct a solution by an iterative procedure.  2002 Elsevier Science (USA). All rights reserved