IDEAS home Printed from https://ideas.repec.org/p/chf/rpseri/rp1953.html
   My bibliography  Save this paper

Properly Discounted Asset Prices Are Semimartingales

Author

Listed:
  • Dániel Ágoston Bálint

    (ETH Zurich - Department of Mathematics)

  • Martin Schweizer

    (ETH Zurich; Swiss Finance Institute)

Abstract

We study general undiscounted asset price processes, which are only assumed to be non-negative, adapted and RCLL (but not a priority semimartingales). Traders are allowed to use simple (piecewise constant) strategies. We prove that under a discounting-invariant condition of absence of arbitrage, the original prices discounted by the value of any simple strategy with positive wealth must follow semimartingales. As a side result, we establish two corresponding versions of the fundamental theorem of asset pricing that involve supermartingale discounters with some additional strict positivity property.

Suggested Citation

  • Dániel Ágoston Bálint & Martin Schweizer, 2019. "Properly Discounted Asset Prices Are Semimartingales," Swiss Finance Institute Research Paper Series 19-53, Swiss Finance Institute.
    • Handle: RePEc:chf:rpseri:rp1953
    as

    Download full text from publisher

    File URL: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3466802
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Kardaras, Constantinos, 2013. "On the closure in the Emery topology of semimartingale wealth-process sets," LSE Research Online Documents on Economics 44996, London School of Economics and Political Science, LSE Library.
    2. Kardaras, Constantinos & Platen, Eckhard, 2011. "On the semimartingale property of discounted asset-price processes," Stochastic Processes and their Applications, Elsevier, vol. 121(11), pages 2678-2691, November.
    3. Constantinos Kardaras, 2011. "On the closure in the Emery topology of semimartingale wealth-process sets," Papers 1108.0945, arXiv.org, revised Jul 2013.
    4. Czichowsky, Christoph & Schachermayer, Walter, 2017. "Portfolio optimisation beyond semimartingales: shadowprices and fractional Brownian motion," LSE Research Online Documents on Economics 67689, London School of Economics and Political Science, LSE Library.
    5. Mathias Beiglbock & Walter Schachermayer & Bezirgen Veliyev, 2010. "A Direct Proof of the Bichteler--Dellacherie Theorem and Connections to Arbitrage," Papers 1004.5559, arXiv.org.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Christoph Kuhn & Alexander Molitor, 2020. "Semimartingale price systems in models with transaction costs beyond efficient friction," Papers 2001.03190, arXiv.org, revised Aug 2021.
    2. Eckhard Platen & Stefan Tappe, 2020. "The Fundamental Theorem of Asset Pricing for Self-Financing Portfolios," Research Paper Series 411, Quantitative Finance Research Centre, University of Technology, Sydney.
    3. Eckhard Platen & Stefan Tappe, 2020. "No arbitrage and multiplicative special semimartingales," Papers 2005.05575, arXiv.org, revised Sep 2022.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Mostovyi, Oleksii, 2020. "Asymptotic analysis of the expected utility maximization problem with respect to perturbations of the numéraire," Stochastic Processes and their Applications, Elsevier, vol. 130(7), pages 4444-4469.
    2. Constantinos Kardaras, 2011. "On the closure in the Emery topology of semimartingale wealth-process sets," Papers 1108.0945, arXiv.org, revised Jul 2013.
    3. Huy N. Chau & Andrea Cosso & Claudio Fontana & Oleksii Mostovyi, 2015. "Optimal investment with intermediate consumption under no unbounded profit with bounded risk," Papers 1509.01672, arXiv.org, revised Jun 2017.
    4. Kardaras, Constantinos, 2013. "On the closure in the Emery topology of semimartingale wealth-process sets," LSE Research Online Documents on Economics 44996, London School of Economics and Political Science, LSE Library.
    5. Oleksii Mostovyi & Mihai Sîrbu, 2019. "Sensitivity analysis of the utility maximisation problem with respect to model perturbations," Finance and Stochastics, Springer, vol. 23(3), pages 595-640, July.
    6. Yuri Kabanov & Constantinos Kardaras & Shiqi Song, 2016. "No arbitrage of the first kind and local martingale numéraires," Finance and Stochastics, Springer, vol. 20(4), pages 1097-1108, October.
    7. Likuan Qin & Vadim Linetsky, 2014. "Long Term Risk: A Martingale Approach," Papers 1411.3078, arXiv.org, revised Oct 2016.
    8. Christa Cuchiero & Irene Klein & Josef Teichmann, 2014. "A new perspective on the fundamental theorem of asset pricing for large financial markets," Papers 1412.7562, arXiv.org, revised Oct 2023.
    9. Sara Biagini & Bruno Bouchard & Constantinos Kardaras & Marcel Nutz, 2014. "Robust Fundamental Theorem for Continuous Processes," Papers 1410.4962, arXiv.org, revised Jul 2015.
    10. Dániel Ágoston Bálint & Martin Schweizer, 2018. "Making No-Arbitrage Discounting-Invariant: A New FTAP Beyond NFLVR and NUPBR," Swiss Finance Institute Research Paper Series 18-23, Swiss Finance Institute, revised Mar 2018.
    11. Christoph Kuhn & Alexander Molitor, 2020. "Semimartingale price systems in models with transaction costs beyond efficient friction," Papers 2001.03190, arXiv.org, revised Aug 2021.
    12. Dirk Becherer & Todor Bilarev & Peter Frentrup, 2017. "Stability for gains from large investors' strategies in M1/J1 topologies," Papers 1701.02167, arXiv.org, revised Mar 2018.
    13. Christoph Kühn & Alexander Molitor, 2022. "Semimartingale price systems in models with transaction costs beyond efficient friction," Finance and Stochastics, Springer, vol. 26(4), pages 927-982, October.
    14. Christa Cuchiero & Josef Teichmann, 2015. "A convergence result for the Emery topology and a variant of the proof of the fundamental theorem of asset pricing," Finance and Stochastics, Springer, vol. 19(4), pages 743-761, October.
    15. Oleksii Mostovyi, 2014. "Utility maximization in the large markets," Papers 1403.6175, arXiv.org, revised Oct 2014.
    16. Sara Biagini & Bruno Bouchard & Constantinos Kardaras & Marcel Nutz, 2017. "Robust Fundamental Theorem for Continuous Processes," Post-Print hal-01076062, HAL.
    17. Kreher, Dörte, 2017. "Change of measure up to a random time: Details," Stochastic Processes and their Applications, Elsevier, vol. 127(5), pages 1565-1598.
    18. Christoph Belak & Lukas Mich & Frank T. Seifried, 2019. "Optimal Investment for Retail Investors with Flooredand Capped Costs," Working Paper Series 2019-06, University of Trier, Research Group Quantitative Finance and Risk Analysis.
    19. Constantinos Kardaras & Jan Obłój & Eckhard Platen, 2017. "The Numéraire Property And Long-Term Growth Optimality For Drawdown-Constrained Investments," Mathematical Finance, Wiley Blackwell, vol. 27(1), pages 68-95, January.

    More about this item

    Keywords

    semimartingales; discounting; dynamic share viability; simple strategies; noshort-sales constraints; NA1 for simple strategies; supermartingale discounter;
    All these keywords.

    JEL classification:

    • C00 - Mathematical and Quantitative Methods - - General - - - General
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:chf:rpseri:rp1953. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Ridima Mittal (email available below). General contact details of provider: https://edirc.repec.org/data/fameech.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.