On the lack of semimartingale property

Vilmos Prokaj and László Bondici

Stochastic Processes and their Applications, 2022, vol. 146, issue C, 335-359

Abstract: In this work we extend the characterization of semimartingale functions in Çinlar et al. (1980) to the non-Markovian setting. We prove that if a function of a semimartingale remains a semimartingale, then under certain conditions the function must have intervals where it is a difference of two convex functions. Under suitable conditions this property also holds for random functions. As an application, we prove that the median process defined in Prokaj et al. (2011) is not a semimartingale. The same process appears also in Hu and Warren (2000) where the question of the semimartingale property is raised but not settled.

Keywords: Semimartingale property; Semimartingale function (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1016/j.spa.2022.01.009

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