DOI 10.1007/s10986-018-9395-2 Lithuanian Mathematical Journal On the quadratic variation of the model-free price paths with jumps a,1 b,2 a,1 Lesiba Charles Galane , Rafał Marcin Łochowski , and Farai Julius Mhlanga Department of Mathematics and Applied Mathematics, University of Limpopo, Private Bag X1106, Sovenga, 0727, South Africa Department of Mathematics and Mathematical Economics, Warsaw School of Economics, ul. Madalins ´ kiego 6/8, 02-513 Warszawa, Poland (e-mail: firstname.lastname@example.org; email@example.com; firstname.lastname@example.org) Received January 18, 2018; revised May 14, 2018 Abstract. We prove that the model-free typical (in the sense of Vovk) càdlàg price paths with mildly restricted downward jumps possess quadratic variation, which does not depend on the speciﬁc sequence of partitions as long as these partitions are obtained from stopping times such that the oscillations of a path on the consecutive (half-open on the right) intervals of these partitions tend (in a speciﬁed sense) to 0. Finally, we also deﬁne quasi-explicit, partition-independent quantities that tend to this quadratic variation. MSC: 60H05, 91G99 Keywords: Vovk’s outer measure, càdlàg price paths, Lebesque partition, quadratic variation, truncated variation 1 Introduction We deal with several properties of the quadratic variation of model-free càdlàg price paths and integrals driven by such paths. Vovk  proved
Lithuanian Mathematical Journal – Springer Journals
Published: Jun 1, 2018
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