On the characterisation of honest times that avoid all stopping times
Probability
2013-05-20 v4
Abstract
We present a short and self-contained proof of the following result: a random time is an honest time that avoids all stopping times if and only if it coincides with the (last) time of maximum of a nonnegative local martingale with zero terminal value and no jumps while at its running supremum, where the latter running supremum process is continuous. Illustrative examples involving local martingales with discontinuous paths are provided.
Cite
@article{arxiv.1202.2882,
title = {On the characterisation of honest times that avoid all stopping times},
author = {Constantinos Kardaras},
journal= {arXiv preprint arXiv:1202.2882},
year = {2013}
}
Comments
12 pages - thoroughly revised version, adding illustrative examples