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Random walk algorithm for the Dirichlet problem for parabolic integro-differential equation

Deligiannidis, G.; Maurer, S.; Tretyakov, M. V.

Random walk algorithm for the Dirichlet problem for parabolic integro-differential equation Thumbnail


Authors

G. Deligiannidis

S. Maurer



Abstract

We consider stochastic differential equations driven by a general Lévy processes (SDEs) with infinite activity and the related, via the Feynman–Kac formula, Dirichlet problem for parabolic integro-differential equation (PIDE). We approximate the solution of PIDE using a numerical method for the SDEs. The method is based on three ingredients: (1) we approximate small jumps by a diffusion; (2) we use restricted jump-adaptive time-stepping; and (3) between the jumps we exploit a weak Euler approximation. We prove weak convergence of the considered algorithm and present an in-depth analysis of how its error and computational cost depend on the jump activity level. Results of some numerical experiments, including pricing of barrier basket currency options, are presented.

Journal Article Type Article
Acceptance Date Mar 26, 2021
Online Publication Date Apr 26, 2021
Publication Date Dec 1, 2021
Deposit Date Mar 16, 2021
Publicly Available Date Apr 27, 2022
Journal BIT Numerical Mathematics
Print ISSN 0006-3835
Electronic ISSN 1572-9125
Publisher Springer Verlag
Peer Reviewed Peer Reviewed
Volume 61
Issue 4
Pages 1223-1269
DOI https://doi.org/10.1007/s10543-021-00863-2
Keywords Computer Networks and Communications; Software; Applied Mathematics; Computational Mathematics
Public URL https://nottingham-repository.worktribe.com/output/5397449
Publisher URL https://link.springer.com/article/10.1007%2Fs10543-021-00863-2

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