Euler–Poisson Schemes for Lévy Processes

Ferreiro-Castilla, Albert

doi:10.1007/978-3-319-51753-7_18

Cited by 1 publication

(2 citation statements)

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“…It is clear how to accomplish this in the context of stochastic differential equations driven by Brownian motion introduced in [10] (see also [18]), where coarse icrements are obtained by summing the fine increments, but it is non-trivial how to proceed in the context of SDEs purely driven by general Lévy processes. A technique based on Poisson thinning has been suggested by [11] for pure-jump diffusion and by [9] for general Lévy processes. In the next section, we explain an alternative construction of a coupled kernel based on the Lévy-Ito decomposition, in the same spirit as in [7].…”

Section: Multilevel Monte Carlo Methodsmentioning

confidence: 99%

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Multilevel particle filters for Lévy-driven stochastic differential equations

2018

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We develop algorithms for computing expectations with respect to the laws of models associated to stochastic differential equations (SDEs) driven by pure Lévy processes. We consider filtering such processes and well as pricing of path dependent options. We propose a multilevel particle filter (MLPF) to address the computational issues involved in solving these continuum problems. We show via numerical simulations and theoretical results that under suitable assumptions regarding the discretization of the underlying driving Lévy proccess, our proposed method achieves optimal convergence rates: the cost to obtain MSE O( 2 ) scales like O( −2 ) for our method, as compared with the standard particle filter O( −3 ).

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Section: Multilevel Monte Carlo Methodsmentioning

confidence: 99%

“…This first work was extended in [6] to a method with a Gaussian correction term which can substantially improve the rate for pure jump processes [2]. The authors in [9] use the MLMC method for general Lévy processes based on Wiener-Hopf decomposition. We extend the methodology described in [7] to a particle filtering framework.…”

Section: Introductionmentioning

confidence: 99%