  In mathematical finance a popular approach for pricing options under some
Levy model is to consider underlying that follows a Poisson jump diffusion
process. As it is well known this results in a partial integro-differential
equation (PIDE) that usually does not allow an analytical solution while
numerical solution brings some problems. In this paper we elaborate a new
approach on how to transform the PIDE to some class of so-called
pseudo-parabolic equations which are known in mathematics but are relatively
new for mathematical finance. As an example we discuss several jump-diffusion
models which Levy measure allows such a transformation.
