Implementable coupling of Lévy process and Brownian motion

Vladimir Fomichov, Jorge González Cázares*, Jevgenijs Ivanovs

*Corresponding author af dette arbejde

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Abstract

We provide a simple algorithm for construction of Brownian paths approximating those of a Lévy process on a finite time interval. It requires knowledge of the Lévy process trajectory on a chosen regular grid and the law of its endpoint, or the ability to simulate from that. This algorithm is based on reordering of Brownian increments, and it can be applied in a recursive manner. We establish an upper bound on the mean squared maximal distance between the paths and determine a suitable mesh size in various asymptotic regimes. The analysis proceeds by reduction to the comonotonic coupling of increments. Applications to model risk and multilevel Monte Carlo are discussed in detail, and numerical examples are provided.

OriginalsprogEngelsk
TidsskriftStochastic Processes and Their Applications
Vol/bind142
Sider (fra-til)407-431
ISSN0304-4149
DOI
StatusUdgivet - dec. 2021

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