IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1205.6254.html
   My bibliography  Save this paper

No-Arbitrage Pricing for Dividend-Paying Securities in Discrete-Time Markets with Transaction Costs

Author

Listed:
  • Tomasz R. Bielecki
  • Igor Cialenco
  • Rodrigo Rodriguez

Abstract

We prove a version of First Fundamental Theorem of Asset Pricing under transaction costs for discrete-time markets with dividend-paying securities. Specifically, we show that the no-arbitrage condition under the efficient friction assumption is equivalent to the existence of a risk-neutral measure. We derive dual representations for the superhedging ask and subhedging bid price processes of a derivative contract. Our results are illustrated with a vanilla credit default swap contract.

Suggested Citation

  • Tomasz R. Bielecki & Igor Cialenco & Rodrigo Rodriguez, 2012. "No-Arbitrage Pricing for Dividend-Paying Securities in Discrete-Time Markets with Transaction Costs," Papers 1205.6254, arXiv.org, revised Jun 2013.
    • Handle: RePEc:arx:papers:1205.6254
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1205.6254
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. Dimitri De Vallière & Yuri Kabanov & Christophe Stricker, 2007. "No-arbitrage criteria for financial markets with transaction costs and incomplete information," Finance and Stochastics, Springer, vol. 11(2), pages 237-251, April.
    3. Saul Jacka & Abdelkarem Berkaoui & Jon Warren, 2008. "No arbitrage and closure results for trading cones with transaction costs," Finance and Stochastics, Springer, vol. 12(4), pages 583-600, October.
    4. repec:dau:papers:123456789/5630 is not listed on IDEAS
    5. Harrison, J. Michael & Pliska, Stanley R., 1981. "Martingales and stochastic integrals in the theory of continuous trading," Stochastic Processes and their Applications, Elsevier, vol. 11(3), pages 215-260, August.
    6. Bruno Bouchard, 2006. "No-arbitrage in Discrete-time Markets with Proportional Transaction Costs and General Information structure," Finance and Stochastics, Springer, vol. 10(2), pages 276-297, April.
    7. Bruno Bouchard, 2006. "No-arbitrage in Discrete-time Markets with Proportional Transaction Costs and General Information structure," Finance and Stochastics, Springer, vol. 10(2), pages 276-297, April.
    8. Walter Schachermayer, 2004. "The Fundamental Theorem of Asset Pricing under Proportional Transaction Costs in Finite Discrete Time," Mathematical Finance, Wiley Blackwell, vol. 14(1), pages 19-48, January.
    9. Nizar Touzi, 1999. "Super-replication under proportional transaction costs: From discrete to continuous-time models," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 50(2), pages 297-320, October.
    10. repec:dau:papers:123456789/4652 is not listed on IDEAS
    11. repec:dau:papers:123456789/9714 is not listed on IDEAS
    12. HuyËn Pham & Nizar Touzi & Jaksa Cvitanic, 1999. "A closed-form solution to the problem of super-replication under transaction costs," Finance and Stochastics, Springer, vol. 3(1), pages 35-54.
    13. J. Jacod & A.N. Shiryaev, 1998. "Local martingales and the fundamental asset pricing theorems in the discrete-time case," Finance and Stochastics, Springer, vol. 2(3), pages 259-273.
    14. Emmanuel Denis & Yuri Kabanov, 2012. "Consistent price systems and arbitrage opportunities of the second kind in models with transaction costs," Finance and Stochastics, Springer, vol. 16(1), pages 135-154, January.
    15. repec:dau:papers:123456789/1533 is not listed on IDEAS
    16. repec:crs:wpaper:9513 is not listed on IDEAS
    17. Schachermayer, W., 1992. "A Hilbert space proof of the fundamental theorem of asset pricing in finite discrete time," Insurance: Mathematics and Economics, Elsevier, vol. 11(4), pages 249-257, December.
    18. Paolo Guasoni & Emmanuel Lépinette & Miklós Rásonyi, 2012. "The fundamental theorem of asset pricing under transaction costs," Finance and Stochastics, Springer, vol. 16(4), pages 741-777, October.
    19. repec:dau:papers:123456789/1850 is not listed on IDEAS
    20. Saul Jacka & Abdelkarem Berkaoui & Jon Warren, 2006. "No-arbitrage and closure results for trading cones with transaction costs," Papers math/0602178, arXiv.org, revised Apr 2008.
    Full references (including those not matched with items on IDEAS)

    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. Christoph Kühn & Alexander Molitor, 2019. "Prospective strict no-arbitrage and the fundamental theorem of asset pricing under transaction costs," Finance and Stochastics, Springer, vol. 23(4), pages 1049-1077, October.
    2. Christoph Kuhn & Alexander Molitor, 2018. "Prospective strict no-arbitrage and the fundamental theorem of asset pricing under transaction costs," Papers 1811.11621, arXiv.org, revised Apr 2019.
    3. Martin Brown & Tomasz Zastawniak, 2020. "Fundamental Theorem of Asset Pricing under fixed and proportional transaction costs," Annals of Finance, Springer, vol. 16(3), pages 423-433, September.
    4. Tomasz R. Bielecki & Igor Cialenco & Ismail Iyigunler & Rodrigo Rodriguez, 2012. "Dynamic Conic Finance: Pricing and Hedging in Market Models with Transaction Costs via Dynamic Coherent Acceptability Indices," Papers 1205.4790, arXiv.org, revised Jun 2013.
    5. Tomasz Zastawniak, 2024. "Fundamental Theorem of Asset Pricing under fixed and proportional costs in multi-asset setting and finite probability space," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 47(1), pages 137-149, June.
    6. Gianluca Cassese, 2017. "Asset pricing in an imperfect world," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 64(3), pages 539-570, October.
    7. Paolo Guasoni & Mikl'os R'asonyi, 2015. "Hedging, arbitrage and optimality with superlinear frictions," Papers 1506.05895, arXiv.org.
    8. Adrien Nguyen Huu, 2011. "A note on super-hedging for investor-producers," Papers 1112.4740, arXiv.org, revised Mar 2012.
    9. repec:cte:wbrepe:wb043513 is not listed on IDEAS
    10. Erindi Allaj, 2017. "Implicit Transaction Costs And The Fundamental Theorems Of Asset Pricing," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(04), pages 1-39, June.
    11. Napp, C., 2003. "The Dalang-Morton-Willinger theorem under cone constraints," Journal of Mathematical Economics, Elsevier, vol. 39(1-2), pages 111-126, February.
    12. Dylan Possamai & Guillaume Royer, 2014. "General indifference pricing with small transaction costs," Papers 1401.3261, arXiv.org, revised Apr 2015.
    13. Kabanov, Yu. M. & Stricker, Ch., 2001. "The Harrison-Pliska arbitrage pricing theorem under transaction costs," Journal of Mathematical Economics, Elsevier, vol. 35(2), pages 185-196, April.
    14. Lepinette, Emmanuel & Tran, Tuan, 2017. "Arbitrage theory for non convex financial market models," Stochastic Processes and their Applications, Elsevier, vol. 127(10), pages 3331-3353.
    15. Gianluca Cassese, 2014. "Option Pricing in an Imperfect World," Papers 1406.0412, arXiv.org, revised Sep 2016.
    16. Dilip B. Madan, 2016. "Benchmarking in two price financial markets," Annals of Finance, Springer, vol. 12(2), pages 201-219, May.
    17. Irene Klein & Emmanuel Lépinette & Lavinia Perez-Ostafe, 2014. "Asymptotic arbitrage with small transaction costs," Finance and Stochastics, Springer, vol. 18(4), pages 917-939, October.
    18. Bentahar, Imen & Bouchard, Bruno, 2005. "Explicit characterization of the super-replication strategy in financial markets with partial transaction costs," SFB 649 Discussion Papers 2005-053, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    19. Patrick Bei{ss}ner, 2012. "Coherent Price Systems and Uncertainty-Neutral Valuation," Papers 1202.6632, arXiv.org.
    20. 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.
    21. Jos'e Manuel Corcuera, 2021. "The Golden Age of the Mathematical Finance," Papers 2102.06693, arXiv.org, revised Mar 2021.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:arx:papers:1205.6254. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.