Coupling and tracking of regime-switching martingales
Abstract
This paper describes two explicit couplings of standard Brownian motions and , 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.
Keywords
Cite
@article{arxiv.1209.0180,
title = {Coupling and tracking of regime-switching martingales},
author = {Saul D. Jacka and Aleksandar Mijatović},
journal= {arXiv preprint arXiv:1209.0180},
year = {2015}
}
Comments
Final version; example in Section 5.2.2 amended; Appendix B, containing new examples of (stopped) Markov chains, added; 39 pages; no figures; appeared in EJP