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Scaling limits of processes with fast nonlinear mean reversion

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Cayé, Thomas, Herdegen, Martin and Muhle-Karbe, Johannes (2020) Scaling limits of processes with fast nonlinear mean reversion. Stochastic Processes and their Applications, 130 (4). pp. 1994-2031. doi:10.1016/j.spa.2019.06.008 ISSN 0304-4149.

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Official URL: http://doi.org/10.1016/j.spa.2019.06.008

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Abstract

We derive scaling limits for integral functionals of Itô processes with fast nonlinear mean-reversion speeds. In these limits, the fast mean-reverting process is “averaged out” by integrating against its invariant measure. The convergence is uniformly in probability and, under mild integrability conditions, also in . These results are a crucial building block for the analysis of portfolio choice models with small superlinear transaction costs, carried out in the companion paper of the present study [11].

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Q Science > QC Physics
Divisions: Faculty of Science, Engineering and Medicine > Science > Statistics
Library of Congress Subject Headings (LCSH): Scaling laws (Statistical physics) , Functions, Entire
Journal or Publication Title: Stochastic Processes and their Applications
Publisher: Elsevier Science BV
ISSN: 0304-4149
Official Date: April 2020
Dates:
DateEvent
April 2020Published
17 June 2019Available
8 June 2019Accepted
Volume: 130
Number: 4
Page Range: pp. 1994-2031
DOI: 10.1016/j.spa.2019.06.008
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access
Date of first compliant deposit: 18 July 2019
Date of first compliant Open Access: 17 June 2020
RIOXX Funder/Project Grant:
Project/Grant IDRIOXX Funder NameFunder ID
150101[SNSF] Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschunghttp://dx.doi.org/10.13039/501100001711
175133[SNSF] Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschunghttp://dx.doi.org/10.13039/501100001711
UNSPECIFIEDImperial College Londonhttp://dx.doi.org/10.13039/501100000761

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