Variational and Topological Methods: Theory, Applications,
Numerical Simulations, and Open Problems.
Electron. J. Diff. Eqns., Conference 21 (2014), pp. 7186.
Existence, uniqueness and numerical approximation of solutions to a
nonlinear integrodifferential equation which arises in option pricing theory
Carsten Erdmann
Abstract:
This article studies the existence and uniqueness of solutions for a fully
nonlinear BlackScholes equation which arises in option pricing theory
in connection with the jump and equilibrium model approach by using
deltahedging arguments. We prove existence and uniqueness for this
nonlinear integrodifferential 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; BlackScholes equations; fully nonlinear equation,
integrodifferential equation.
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Carsten Erdmann
Institute of Mathematics
Ulmenstras e 69
Haus 3, 18057 Rostock, Germany
email: dr@carstenerdmann.de

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