Abstract
In this note we will contextualize the recently established Wiener–Hopf Monte Carlo (WHMC) simulation technique for Lévy processes from Kuznetsov et al. (Ann Appl Probab 21(6):2171–2190, 2011), into a more general framework allowing us to use the same technique in a larger set of problems. We will briefly show how the scheme can be used to approximate Lévy driven SDEs or how to approximate different types of path dependent quantities. In a way, the present note summarizes and connects a set of results contained in Ferreiro-Castilla et al. (Stochastic Process Appl 124(2):985–1010, 2014; J Appl Probab 52(1):129–148, 2015; J Appl Probab 53(1):262–278, 2016); therefore we intentionally leave most of the technicalities aside for this note.
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Acknowledgements
Part of this research was supported by a Royal Society Newton International Fellowship.
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Ferreiro-Castilla, A. (2017). Euler–Poisson Schemes for Lévy Processes. In: Díaz, J., Kirousis, L., Ortiz-Gracia, L., Serna, M. (eds) Extended Abstracts Summer 2015. Trends in Mathematics(), vol 6. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-51753-7_18
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