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Coupling and tracking of regime-switching martingales
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Jacka, Saul D. and Mijatović, Aleksandar (2015) Coupling and tracking of regime-switching martingales. Electronic Journal of Probability, 20 . pp. 1-39. 38. doi:10.1214/EJP.v20-2307 ISSN 1083-6489.
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Official URL: http://dx.doi.org/10.1214/EJP.v20-2307
Abstract
This paper describes two explicit couplings of standard Brownian motions BB and VV, which naturally extend the mirror coupling and the synchronous coupling and respectively maximise and minimise (uniformly over all time horizons) the coupling time and the tracking error of two regime-switching martingales. The generalised mirror coupling minimizes the coupling time of the two martingales while simultaneously maximising the tracking error for all time horizons. The generalised synchronous coupling maximises the coupling time and minimises the tracking error over all co-adapted couplings. The proofs are based on the Bellman principle. We give counterexamples to the conjectured optimality of the two couplings amongst a wider classes of stochastic integrals.
Item Type: | Journal Article | ||||||
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Subjects: | Q Science > QA Mathematics | ||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||||
Library of Congress Subject Headings (LCSH): | Brownian movements , Markov processes, Martingales (Mathematics), Stochastic analysis | ||||||
Journal or Publication Title: | Electronic Journal of Probability | ||||||
Publisher: | University of Washington. Dept. of Mathematics | ||||||
ISSN: | 1083-6489 | ||||||
Official Date: | 1 April 2015 | ||||||
Dates: |
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Volume: | 20 | ||||||
Page Range: | pp. 1-39 | ||||||
Article Number: | 38 | ||||||
DOI: | 10.1214/EJP.v20-2307 | ||||||
Status: | Peer Reviewed | ||||||
Publication Status: | Published | ||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||
Date of first compliant deposit: | 14 January 2016 | ||||||
Date of first compliant Open Access: | 14 January 2016 |
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