Strong approximations of stochastic differential equations with jumps

Authors:
Nicola Bruti-Liberati;Eckhard Platen
Affiliations:
School of Finance and Economics, Australia;Department of Mathematical Sciences, School of Finance and Economics, University of Technology, Sydney, PO Box 123, Broadway, NSW 2007, Australia
Venue:
Journal of Computational and Applied Mathematics
Year:
2007

Citing 3
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Abstract

This paper is a survey of strong discrete time approximations of jump-diffusion processes described by stochastic differential equations (SDEs). It also presents new results on strong discrete time approximations for the specific case of pure jump SDEs. Strong approximations based on jump-adapted time discretizations, which produce no discretization error in the case of pure jump processes, are analyzed. The computational complexity of these approximations is proportional to the jump intensity. By exploiting a stochastic expansion for pure jump processes, higher order discrete time approximations, whose computational complexity is not dependent on the jump intensity, are proposed. For the specific case of pure jump SDEs, the strong order of convergence of strong Taylor schemes is established under weaker conditions than those currently known in the literature.