The Riesz representation theorem and weak∗ compactness of semimartingales

Matti Kiiski ()
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Matti Kiiski: University of Mannheim

Finance and Stochastics, 2020, vol. 24, issue 4, No 1, 827-870

Abstract: Abstract We show that the sequential closure of a family of probability measures on the canonical space of càdlàg paths satisfying Stricker’s uniform tightness condition is a weak∗ compact set of semimartingale measures in the dual pairing of bounded continuous functions and Radon measures, that is, the dual pairing from the Riesz representation theorem under topological assumptions on the path space. Similar results are obtained for quasi- and supermartingales under analogous conditions. In particular, we give a full characterisation of the strongest topology on the Skorokhod space for which these results are true.

Keywords: Skorokhod space; Meyer–Zheng topology; S $S$ -topology; Weak∗ topology; Càdlàg semimartingale; 28C05; 54D30; 60B05; 60G05 (search for similar items in EconPapers)
JEL-codes: C02 G13 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s00780-020-00432-5

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