On the characterization of honest times avoiding all stopping times

Details On the characterization of honest times avoiding all stopping times On the characterization of honest times avoiding all stopping times

2012-02-13

arxiv.org/abs/1202.2882v2

Mathematics

Probability

5 pages - new version correcting minor mistakes of the original one

Scientific paper

We present a self-contained proof of the following result: a random time is an honest time avoiding all stopping times if and only if it coincides with the (first) time that a nonnegative local martingale with continuous supremum process and zero terminal value achieves its overall maximum, given that this time of maximum is almost surely finite. The requirement that all martingales on the stochastic basis have continuous paths, which was present in previous literature, is dropped.

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