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The Riesz representation theorem and weak∗ compactness of semimartingales

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  • Matti Kiiski

    (University of Mannheim)

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.

Suggested Citation

  • Matti Kiiski, 2020. "The Riesz representation theorem and weak∗ compactness of semimartingales," Finance and Stochastics, Springer, vol. 24(4), pages 827-870, October.
    • Handle: RePEc:spr:finsto:v:24:y:2020:i:4:d:10.1007_s00780-020-00432-5
    DOI: 10.1007/s00780-020-00432-5
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    References listed on IDEAS

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    1. ,, 2001. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 17(6), pages 1157-1160, December.
    2. Y. Dolinsky & H. M. Soner, 2014. "Martingale optimal transport in the Skorokhod space," Papers 1404.1516, arXiv.org, revised Feb 2015.
    3. Guo, Gaoyue & Tan, Xiaolu & Touzi, Nizar, 2017. "Tightness and duality of martingale transport on the Skorokhod space," Stochastic Processes and their Applications, Elsevier, vol. 127(3), pages 927-956.
    4. Dolinsky, Yan & Soner, H. Mete, 2015. "Martingale optimal transport in the Skorokhod space," Stochastic Processes and their Applications, Elsevier, vol. 125(10), pages 3893-3931.
    5. ,, 2001. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 17(5), pages 1025-1031, October.
    6. Mathias Beiglböck & Pierre Henry-Labordère & Friedrich Penkner, 2013. "Model-independent bounds for option prices—a mass transport approach," Finance and Stochastics, Springer, vol. 17(3), pages 477-501, July.
    7. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    8. Patrick Cheridito & Matti Kiiski & David J. Promel & H. Mete Soner, 2019. "Martingale optimal transport duality," Papers 1904.04644, arXiv.org, revised Nov 2020.
    9. Mathias Beiglbock & Pierre Henry-Labord`ere & Friedrich Penkner, 2011. "Model-independent Bounds for Option Prices: A Mass Transport Approach," Papers 1106.5929, arXiv.org, revised Feb 2013.
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    More about this item

    Keywords

    Skorokhod space; Meyer–Zheng topology; S $S$ -topology; Weak∗ topology; Càdlàg semimartingale;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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