Strong approximations of stochastic differential equations with jumps

NicolaBruti-Liberati and Eckhard Platen ()

Published Paper Series from Finance Discipline Group, UTS Business School, University of Technology, Sydney

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.

Keywords: Jump-diffusion processes; Pure jump processes; Stochastic Taylor expansion; Discrete time approximation; Simulation; Strong convergence (search for similar items in EconPapers)
Pages: 20 pages
Date: 2007-01-01
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Citations: View citations in EconPapers (11)

Published in: Bruti Liberati, N. and Platen, E., 2007, "Strong Approximations of Stochastic Differential Equations with Jumps", Journal of Computational and Applied Mathematics, 205(2), 982-1001.

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