Characterization of max-continuous local martingales vanishing at infinity

2014/12/03 by Beatrice Acciaio, Acciaio, Beatrice, Irina Penner +1
Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #math.PR

paper · pdf · doi:10.48550/arxiv.1412.1366

openalex publication_date 2014/12/03 · arxiv created 2016/09/30 · arxiv updated 2016/10/03 · openalex created_date 2022/10/07 · openalex updated_date 2026/07/28

Abstract

We provide a characterization of the family of non-negative local martingales that have continuous running supremum and vanish at infinity. This is done by describing the class of random times that identify the times of maximum of such processes. In this way we extend to the case of general filtrations a result proved by Nikeghbali and Yor [NY06] for continuous filtrations. Our generalization is complementary to the one presented by Kardaras [Kar14], and is obtained by means of similar tools.

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