Variational and Topological Methods: Theory, Applications, 
Numerical Simulations, and Open Problems.
Electron. J. Diff. Eqns., Conference 21 (2014), pp. 77-86.

Title: Existence, uniqueness and numerical approximation of solutions to a
       nonlinear integro-differential equation which arises in option pricing theory

Author: Carsten Erdmann (Institute of Mathematics, Rostock, Germany)
 
Abstract: 
 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.

Published February 10, 2014.
Math Subject Classifications: 35K15, 35K67, 91G80.
Key Words: Option pricing; Black-Scholes equations; fully nonlinear equation,
           integro-differential equation.