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 regimes.Therefore, we study the asymptotic time behavior of such equations and we define as 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.
"Asymptotic high-order schemes for integro-differential problems arising in markets with jumps." Commun. Math. Sci. 4 (1) 81 - 96, March 2006.