August  2010, 27(3): 907-917. doi: 10.3934/dcds.2010.27.907

A nonlinear partial integro-differential equation from mathematical finance

1. 

Grande Voie des Vignes, Chatenay-Malabry, 92295, France, France

Received  July 2009 Revised  January 2010 Published  March 2010

Consistently fitting vanilla option surfaces is an important issue when it comes to modeling in finance. As far as local and stochastic volatility models are concerned, this problem boils down to the resolution of a nonlinear integro-differential pde. The non-locality of this equation stems from the quotient of two integral terms and is not defined for all bounded continuous functions. In this paper, we use a fixed point argument and suitable a priori estimates to prove short-time existence of solutions for this equation.
Citation: Frederic Abergel, Remi Tachet. A nonlinear partial integro-differential equation from mathematical finance. Discrete and Continuous Dynamical Systems, 2010, 27 (3) : 907-917. doi: 10.3934/dcds.2010.27.907
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