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Abstract: In mathematical finance a popular approach for pricing options under someLevy model is to consider underlying that follows a Poisson jump diffusionprocess. As it is well known this results in a partial integro-differentialequation PIDE that usually does not allow an analytical solution whilenumerical solution brings some problems. In this paper we elaborate a newapproach on how to transform the PIDE to some class of so-calledpseudo-parabolic equations which are known in mathematics but are relativelynew for mathematical finance. As an example we discuss several jump-diffusionmodels which Levy measure allows such a transformation.



Author: Andrey Itkin, Peter Carr

Source: https://arxiv.org/



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