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Exact simulation of gamma-driven Ornstein–Uhlenbeck processes with finite and infinite activity jumps
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Qu, Yan, Dassios, Angelos and Zhao, Hongbiao (2021) Exact simulation of gamma-driven Ornstein–Uhlenbeck processes with finite and infinite activity jumps. Journal of the Operational Research Society, 72 (2). pp. 471-484. doi:10.1080/01605682.2019.1657368 ISSN 0160-5682.
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WRAP-exact-simulation-gamma-driven-finite-activity-jumps-Qu-2020.pdf - Accepted Version - Requires a PDF viewer. Download (1101Kb) | Preview |
Official URL: https://doi.org/10.1080/01605682.2019.1657368
Abstract
We develop a distributional decomposition approach for exactly simulating two types of Gamma-driven Ornstein–Uhlenbeck (OU) processes with time-varying marginal distributions: the Gamma-OU process and the OU-Gamma process. The former has finite-activity jumps, and its marginal distribution is asymptotically Gamma; the latter has infinite-activity jumps that are driven by a Gamma process. We prove that the transition distributions of the two processes at any given time can be exactly decomposed into simple elements: at any given time, the former is equal in distribution to the sum of one deterministic trend and one compound Poisson random variable (r.v.); the latter is equal in distribution to the sum of one deterministic trend, one compound Poisson r.v., and one Gamma r.v. The results immediately lead to very efficient algorithms for their exact simulations without numerical inversion. Extensive numerical experiments are reported to demonstrate the accuracy and efficiency of
our algorithms.
| Item Type: | Journal Article | |||||||||
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| Subjects: | Q Science > QA Mathematics T Technology > T Technology (General) |
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| Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | |||||||||
| Library of Congress Subject Headings (LCSH): | Monte Carlo method , Perfect simulation (Statistics) , Gaussian processes, Ornstein-Uhlenbeck process | |||||||||
| Journal or Publication Title: | Journal of the Operational Research Society | |||||||||
| Publisher: | Taylor & Francis (Routledge) | |||||||||
| ISSN: | 0160-5682 | |||||||||
| Official Date: | 2021 | |||||||||
| Dates: |
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| Volume: | 72 | |||||||||
| Number: | 2 | |||||||||
| Page Range: | pp. 471-484 | |||||||||
| DOI: | 10.1080/01605682.2019.1657368 | |||||||||
| Status: | Peer Reviewed | |||||||||
| Publication Status: | Published | |||||||||
| Reuse Statement (publisher, data, author rights): | “This is an Accepted Manuscript of an article published by Taylor & Francis in Journal of the Operational Research Society on 20/12/2019, available online: http://www.tandfonline.com/10.1080/01605682.2019.1657368 | |||||||||
| Access rights to Published version: | Restricted or Subscription Access | |||||||||
| Date of first compliant deposit: | 5 February 2020 | |||||||||
| Date of first compliant Open Access: | 20 December 2020 | |||||||||
| RIOXX Funder/Project Grant: |
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