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Mirror and synchronous couplings of geometric Brownian motions
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Jacka, Saul D., Mijatović, Aleksandar and Širaj, Dejan (2014) Mirror and synchronous couplings of geometric Brownian motions. Stochastic Processes and their Applications, Volume 124 (Number 2). pp. 1055-1069. doi:10.1016/j.spa.2013.10.003 ISSN 0304-4149.
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Official URL: http://dx.doi.org/10.1016/j.spa.2013.10.003
Abstract
The paper studies the question of whether the classical mirror and synchronous couplings of two Brownian motions minimise and maximise, respectively, the coupling time of the corresponding geometric Brownian motions. We establish a characterisation of the optimality of the two couplings over any finite time horizon and show that, unlike in the case of Brownian motion, the optimality fails in general even if the geometric Brownian motions are martingales. On the other hand, we prove that in the cases of the ergodic average and the infinite time horizon criteria, the mirror coupling and the synchronous coupling are always optimal for general (possibly non-martingale) geometric Brownian motions. We show that the two couplings are efficient if and only if they are optimal over a finite time horizon and give a conjectural answer for the efficient couplings when they are suboptimal.
Item Type: | Journal Article | ||||||||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||||||||
Journal or Publication Title: | Stochastic Processes and their Applications | ||||||||||
Publisher: | Elsevier Science BV | ||||||||||
ISSN: | 0304-4149 | ||||||||||
Official Date: | February 2014 | ||||||||||
Dates: |
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Volume: | Volume 124 | ||||||||||
Number: | Number 2 | ||||||||||
Page Range: | pp. 1055-1069 | ||||||||||
DOI: | 10.1016/j.spa.2013.10.003 | ||||||||||
Status: | Peer Reviewed | ||||||||||
Publication Status: | Published | ||||||||||
Access rights to Published version: | Restricted or Subscription Access |
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