On the quadratic variation of the model-free price paths with jumps

On the quadratic variation of the model-free price paths with jumps 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: lesiba.galane@ul.ac.za; rlocho@sgh.waw.pl; farai.mhlanga@ul.ac.za) 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 [12] proved http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Lithuanian Mathematical Journal Springer Journals

On the quadratic variation of the model-free price paths with jumps

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Publisher
Springer Journals
Copyright
Copyright © 2018 by Springer Science+Business Media, LLC, part of Springer Nature
Subject
Mathematics; Mathematics, general; Ordinary Differential Equations; Actuarial Sciences; Number Theory; Probability Theory and Stochastic Processes
ISSN
0363-1672
eISSN
1573-8825
D.O.I.
10.1007/s10986-018-9395-2
Publisher site
See Article on Publisher Site

Abstract

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: lesiba.galane@ul.ac.za; rlocho@sgh.waw.pl; farai.mhlanga@ul.ac.za) 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 [12] proved

Journal

Lithuanian Mathematical JournalSpringer Journals

Published: Jun 1, 2018

References

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