IDEAS home Printed from https://ideas.repec.org/a/spr/finsto/v23y2019i2d10.1007_s00780-019-00386-3.html
   My bibliography  Save this article

Some no-arbitrage rules under short-sales constraints, and applications to converging asset prices

Author

Listed:
  • Delia Coculescu

    (University of Zurich)

  • Monique Jeanblanc

    (Université d’Evry Val d’Essonne)

Abstract

Under short-sales prohibitions, no free lunch with vanishing risk (NFLVRS) is known to be equivalent to the existence of an equivalent supermartingale measure for the price process (Pulido in Ann. Appl. Probab. 24:54–75, 2014). We give a necessary condition for the drift of a price process to satisfy NFLVRS. For two given price processes, we introduce the concept of fundamental supermartingale measure, and when a certain condition necessary for the construction of this fundamental supermartingale measure is not fulfilled, we provide the corresponding arbitrage portfolios. The motivation of our study lies in understanding the particular case of converging prices, i.e., two prices that coincide at a bounded random time.

Suggested Citation

  • Delia Coculescu & Monique Jeanblanc, 2019. "Some no-arbitrage rules under short-sales constraints, and applications to converging asset prices," Finance and Stochastics, Springer, vol. 23(2), pages 397-421, April.
    • Handle: RePEc:spr:finsto:v:23:y:2019:i:2:d:10.1007_s00780-019-00386-3
    DOI: 10.1007/s00780-019-00386-3
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00780-019-00386-3
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00780-019-00386-3?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Napp, C., 2003. "The Dalang-Morton-Willinger theorem under cone constraints," Journal of Mathematical Economics, Elsevier, vol. 39(1-2), pages 111-126, February.
    2. Jouini Elyes & Kallal Hedi, 1995. "Martingales and Arbitrage in Securities Markets with Transaction Costs," Journal of Economic Theory, Elsevier, vol. 66(1), pages 178-197, June.
    3. Pham, Huyen & Touzi, Nizar, 1999. "The fundamental theorem of asset pricing with cone constraints," Journal of Mathematical Economics, Elsevier, vol. 31(2), pages 265-279, March.
    4. R. J. Elliott & M. Jeanblanc & M. Yor, 2000. "On Models of Default Risk," Mathematical Finance, Wiley Blackwell, vol. 10(2), pages 179-195, April.
    5. Ioannis Karatzas & Constantinos Kardaras, 2007. "The numéraire portfolio in semimartingale financial models," Finance and Stochastics, Springer, vol. 11(4), pages 447-493, October.
    6. Schweizer, Martin, 1992. "Martingale densities for general asset prices," Journal of Mathematical Economics, Elsevier, vol. 21(4), pages 363-378.
    7. repec:dau:papers:123456789/5630 is not listed on IDEAS
    8. Elyégs Jouini & Hédi Kallal, 1995. "Arbitrage In Securities Markets With Short‐Sales Constraints," Mathematical Finance, Wiley Blackwell, vol. 5(3), pages 197-232, July.
    9. Robert Jarrow & Philip Protter & Sergio Pulido, 2015. "The Effect Of Trading Futures On Short Sale Constraints," Mathematical Finance, Wiley Blackwell, vol. 25(2), pages 311-338, April.
    10. Sergio Pulido, 2010. "The fundamental theorem of asset pricing, the hedging problem and maximal claims in financial markets with short sales prohibitions," Papers 1012.3102, arXiv.org, revised Jan 2014.
    11. repec:dau:papers:123456789/5647 is not listed on IDEAS
    12. Back, Kerry, 1991. "Asset pricing for general processes," Journal of Mathematical Economics, Elsevier, vol. 20(4), pages 371-395.
    13. Sergio Pulido, 2014. "The fundamental theorem of asset pricing, the hedging problem and maximal claims in financial markets with short sales prohibitions," Post-Print hal-02265271, HAL.
    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. Delia Coculescu & Aditi Dandapani, 2020. "Insiders and their Free Lunches: the Role of Short Positions," Papers 2012.00359, arXiv.org, revised Jan 2022.
    2. Eckhard Platen & Stefan Tappe, 2020. "Exploiting arbitrage requires short selling," Papers 2011.12523, 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. Delia Coculescu & Monique Jeanblanc, 2017. "Some No-Arbitrage Rules For Converging Asset Prices under Short-Sales Constraints," Papers 1709.09252, arXiv.org.
    2. Delia Coculescu & Aditi Dandapani, 2020. "Insiders and their Free Lunches: the Role of Short Positions," Papers 2012.00359, arXiv.org, revised Jan 2022.
    3. Robert Jarrow & Philip Protter & Sergio Pulido, 2015. "The Effect Of Trading Futures On Short Sale Constraints," Mathematical Finance, Wiley Blackwell, vol. 25(2), pages 311-338, April.
    4. Fontana, Claudio & Runggaldier, Wolfgang J., 2021. "Arbitrage concepts under trading restrictions in discrete-time financial markets," Journal of Mathematical Economics, Elsevier, vol. 92(C), pages 66-80.
    5. Claudio Fontana & Wolfgang J. Runggaldier, 2020. "Arbitrage concepts under trading restrictions in discrete-time financial markets," Papers 2006.15563, arXiv.org, revised Sep 2020.
    6. Sergio Pulido, 2010. "The fundamental theorem of asset pricing, the hedging problem and maximal claims in financial markets with short sales prohibitions," Papers 1012.3102, arXiv.org, revised Jan 2014.
    7. Eckhard Platen & Stefan Tappe, 2020. "Exploiting arbitrage requires short selling," Papers 2011.12523, arXiv.org, revised Sep 2022.
    8. Alet Roux, 2007. "The fundamental theorem of asset pricing under proportional transaction costs," Papers 0710.2758, arXiv.org.
    9. Alexander M. G. Cox & Zhaoxu Hou & Jan Obloj, 2014. "Robust pricing and hedging under trading restrictions and the emergence of local martingale models," Papers 1406.0551, arXiv.org, revised Jun 2015.
    10. Maxim Bichuch & Agostino Capponi & Stephan Sturm, 2016. "Arbitrage-Free XVA," Papers 1608.02690, arXiv.org.
    11. Xiaotie Deng & Zhong Li & Shouyang Wang & Hailiang Yang, 2005. "Necessary and Sufficient Conditions for Weak No-Arbitrage in Securities Markets with Frictions," Annals of Operations Research, Springer, vol. 133(1), pages 265-276, January.
    12. Duffie, Darrell, 2003. "Intertemporal asset pricing theory," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, edition 1, volume 1, chapter 11, pages 639-742, Elsevier.
    13. Arash Fahim & Yu-Jui Huang, 2016. "Model-independent superhedging under portfolio constraints," Finance and Stochastics, Springer, vol. 20(1), pages 51-81, January.
    14. Roux, Alet, 2011. "The fundamental theorem of asset pricing in the presence of bid-ask and interest rate spreads," Journal of Mathematical Economics, Elsevier, vol. 47(2), pages 159-163, March.
    15. Arash Fahim & Yu-Jui Huang, 2016. "Model-independent superhedging under portfolio constraints," Finance and Stochastics, Springer, vol. 20(1), pages 51-81, January.
    16. M. Dempster & I. Evstigneev & M. Taksar, 2006. "Asset Pricing and Hedging in Financial Markets with Transaction Costs: An Approach Based on the Von Neumann–Gale Model," Annals of Finance, Springer, vol. 2(4), pages 327-355, October.
    17. Teemu Pennanen, 2011. "Arbitrage and deflators in illiquid markets," Finance and Stochastics, Springer, vol. 15(1), pages 57-83, January.
    18. Teemu Pennanen, 2014. "Optimal investment and contingent claim valuation in illiquid markets," Finance and Stochastics, Springer, vol. 18(4), pages 733-754, October.
    19. Jochen Wilhelm & Josef Schosser, 2007. "A note on arbitrage-free asset prices with and without personal income taxes," Review of Managerial Science, Springer, vol. 1(2), pages 133-149, August.
    20. Gerber, Hans U. & Shiu, Elias S. W., 1996. "Actuarial bridges to dynamic hedging and option pricing," Insurance: Mathematics and Economics, Elsevier, vol. 18(3), pages 183-218, November.

    More about this item

    Keywords

    Equivalent supermartingale measures; No free lunch with vanishing risk; Short-sales constraints; Converging asset prices;
    All these keywords.

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

    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:spr:finsto:v:23:y:2019:i:2:d:10.1007_s00780-019-00386-3. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.