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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
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    References listed on IDEAS

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    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.
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    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.
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    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Shuzhen Yang & Wenqing Zhang, 2024. "Asset pricing under model uncertainty with finite time and states," Papers 2408.13048, 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. Eckhard Platen & Stefan Tappe, 2020. "Exploiting arbitrage requires short selling," Papers 2011.12523, arXiv.org, revised Sep 2022.

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    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

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