EXISTENCE, UNIQUENESS AND NUMERICAL APPROXIMATION OF SOLUTIONS TO A NONLINEAR INTEGRO-DIFFERENTIAL EQUATION WHICH ARISES IN OPTION PRICING THEORY

This article studies the existence and uniqueness of solutions for a fully nonlinear Black-Scholes equation which arises in option pricing theory in connection with the jump and equilibrium model approach by using delta-hedging arguments. We prove existence and uniqueness for this nonlinear integro-differential equation by using a fixed point method. The convergence of the numerical scheme, which is based on finite differences, is also proved.