IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1902.10492.html
   My bibliography  Save this paper

A convex duality approach for pricing contingent claims under partial information and short selling constraints

Author

Listed:
  • Kristina Rognlien Dahl

Abstract

We consider the pricing problem facing a seller of a contingent claim. We assume that this seller has some general level of partial information, and that he is not allowed to sell short in certain assets. This pricing problem, which is our primal problem, is a constrained stochastic optimization problem. We derive a dual to this problem by using the conjugate duality theory introduced by Rockafellar. Furthermore, we give conditions for strong duality to hold. This gives a characterization of the price of the claim involving martingale- and super-martingale conditions on the optional projection of the price processes.

Suggested Citation

  • Kristina Rognlien Dahl, 2019. "A convex duality approach for pricing contingent claims under partial information and short selling constraints," Papers 1902.10492, arXiv.org.
  • Handle: RePEc:arx:papers:1902.10492
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1902.10492
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. DEVOLDER, Olivier & GLINEUR, François & NESTEROV, Yurii, 2010. "Solving infinite-dimensional optimization problems by polynomial approximation," LIDAM Discussion Papers CORE 2010029, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Frittelli, Marco & Rosazza Gianin, Emanuela, 2002. "Putting order in risk measures," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1473-1486, July.
    3. 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.
    4. Elyégs Jouini & Hédi Kallal, 1995. "Arbitrage In Securities Markets With Short‐Sales Constraints," Mathematical Finance, Wiley Blackwell, vol. 5(3), pages 197-232, July.
    5. repec:dau:papers:123456789/1850 is not listed on IDEAS
    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. repec:dau:papers:123456789/5647 is not listed on IDEAS
    8. 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.
    9. Teemu Pennanen, 2011. "Convex Duality in Stochastic Optimization and Mathematical Finance," Mathematics of Operations Research, INFORMS, vol. 36(2), pages 340-362, May.
    10. Föllmer, Hans & Kramkov, D. O., 1997. "Optional decompositions under constraints," SFB 373 Discussion Papers 1997,31, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    11. I. Klein & L. C. G. Rogers, 2007. "Duality In Optimal Investment And Consumption Problems With Market Frictions," Mathematical Finance, Wiley Blackwell, vol. 17(2), pages 225-247, April.
    12. Ioannis Karatzas & (*), S. G. Kou, 1998. "Hedging American contingent claims with constrained portfolios," Finance and Stochastics, Springer, vol. 2(3), pages 215-258.
    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. Ariel Neufeld & Mario Sikic, 2016. "Robust Utility Maximization in Discrete-Time Markets with Friction," Papers 1610.09230, arXiv.org, revised May 2018.
    2. 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.
    3. 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.
    4. Teemu Pennanen & Ari-Pekka Perkkiö, 2018. "Convex duality in optimal investment and contingent claim valuation in illiquid markets," Finance and Stochastics, Springer, vol. 22(4), pages 733-771, October.
    5. 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.
    6. Peter Bank & Selim Gokay, 2013. "Superreplication when trading at market indifference prices," Papers 1310.3113, arXiv.org.
    7. 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.
    8. 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.
    9. Kristina Rognlien Dahl, 2019. "Management of a hydropower system via convex duality," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 89(1), pages 43-71, February.
    10. Arash Fahim & Yu-Jui Huang, 2014. "Model-independent Superhedging under Portfolio Constraints," Papers 1402.2599, arXiv.org, revised Jun 2015.
    11. Teemu Pennanen & Ari-Pekka Perkkio, 2016. "Convex duality in optimal investment and contingent claim valuation in illiquid markets," Papers 1603.02867, arXiv.org.
    12. Alet Roux, 2007. "The fundamental theorem of asset pricing under proportional transaction costs," Papers 0710.2758, arXiv.org.
    13. Mario Sikic, 2015. "Financial market models in discrete time beyond the concave case," Papers 1512.01758, arXiv.org.
    14. 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.
    15. Nguyen-Thanh Long, 2004. "Investment optimization under constraints," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 60(2), pages 175-201, October.
    16. Bion-Nadal, Jocelyne, 2009. "Bid-ask dynamic pricing in financial markets with transaction costs and liquidity risk," Journal of Mathematical Economics, Elsevier, vol. 45(11), pages 738-750, December.
    17. Dylan Possamai & Guillaume Royer, 2014. "General indifference pricing with small transaction costs," Papers 1401.3261, arXiv.org, revised Apr 2015.
    18. Touzi, Nizar, 2000. "Direct characterization of the value of super-replication under stochastic volatility and portfolio constraints," Stochastic Processes and their Applications, Elsevier, vol. 88(2), pages 305-328, August.
    19. Gianluca Cassese, 2014. "Option Pricing in an Imperfect World," Papers 1406.0412, arXiv.org, revised Sep 2016.
    20. Long Nguyen-Thanh, 2002. "Consumption and Investment Optimization under Constraints," Finance 0211004, University Library of Munich, Germany, revised 25 Mar 2003.

    More about this item

    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:1902.10492. 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.