Asymptotic high-order schemes for integro-differential problems arising in markets with jumps

In this paper we deal with the numerical approximation of
integro-differential equations arising in financial applications
in which jump processes act as the underlying stochastic processes.
Our aim is to find finite differences schemes which are high-order accurate
for large time simulations.
Therefore, we study the asymptotic time behavior of such equations
and we define as {\it asymptotic high-order schemes} those schemes
that are consistent
with this behavior.
Numerical tests are presented to investigate the
efficiency and the accuracy of such approximations.