Variational and Topological Methods: Theory, Applications, Numerical Simulations, and Open Problems.
Electron. J. Diff. Eqns., Conference 21 (2014), pp. 71-86.

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

Carsten Erdmann

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.

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Carsten Erdmann
Institute of Mathematics
Ulmenstras e 69
Haus 3, 18057 Rostock, Germany

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