Multilevel particle filters for Lévy-driven stochastic differential equations

License
https://creativecommons.org/licenses/by/4.0

Type
Article

Authors
Jasra, Ajay
Law, Kody J H
Osei, Prince Peprah

KAUST Grant Number
Competitive Research Grant round 4

Date
2018-10-20

Abstract
We develop algorithms for computing expectations with respect to the laws of models associated to stochastic differential equations driven by pure Lévy processes. We consider filtering such processes as well as pricing of path dependent options. We propose a multilevel particle filter 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, the cost to obtain MSE O(ϵ2) scales like O(ϵ- 2) for our method, as compared with the standard particle filter O(ϵ- 3).

Citation
Jasra, A., Law, K. J. H., & Osei, P. P. (2018). Multilevel particle filters for Lévy-driven stochastic differential equations. Statistics and Computing, 29(4), 775–789. doi:10.1007/s11222-018-9837-z

Acknowledgements
AJ was supported by Singapore ministry of education AcRF tier 2 Grant R-155-00-161-112 and he is affiliated with the CQF, RMI and ORA cluster at NUS. He was also supported by a King Abdullah University of Science and Technology Competitive Research Grant round 4, Ref:2584. KJHL was sponsored by the Laboratory Directed Research and Development Program of Oak Ridge National Laboratory, managed by UT-Battelle, LLC, for the U. S. Department of Energy, as well as the School of Mathematics at the University of Manchester. We would also like to thank the anonymous referees for numerous suggestions and corrections which have greatly improved the manuscript.

Publisher
Springer Nature

Journal
Statistics and Computing

DOI
10.1007/s11222-018-9837-z

arXiv
1804.04444

Additional Links
http://link.springer.com/10.1007/s11222-018-9837-z

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