IDEAS home Printed from https://ideas.repec.org/p/zbw/sfb373/199754.html
   My bibliography  Save this paper

Optional decomposition and lagrange multipliers

Author

Listed:
  • Föllmer, Hans
  • Kabanov, Jurij M.

Abstract

Let Q be the set of equivalent martingale measures for a given process S, and let X be a process which is a local supermartingale with respect to any measure in Q. The optional decomposition theorem for X states that there exists a predictable integrand ф such that the difference X−ф•S is a decreasing process. In this paper we give a new proof which uses techniques from stochastic calculus rather than functional analysis, and which removes any boundedness assumption.

Suggested Citation

  • Föllmer, Hans & Kabanov, Jurij M., 1997. "Optional decomposition and lagrange multipliers," SFB 373 Discussion Papers 1997,54, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    • Handle: RePEc:zbw:sfb373:199754
    as

    Download full text from publisher

    File URL: https://www.econstor.eu/bitstream/10419/66314/1/729464105.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Ernst Eberlein & Jean Jacod, 1997. "On the range of options prices (*)," Finance and Stochastics, Springer, vol. 1(2), pages 131-140.
    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. Frank Bosserhoff & Mitja Stadje, 2019. "Robustness of Delta Hedging in a Jump-Diffusion Model," Papers 1910.08946, arXiv.org, revised Apr 2022.
    2. Bank, Peter & Riedel, Frank, 1999. "Optimal consumption choice under uncertainty with intertemporal substitution," SFB 373 Discussion Papers 1999,71, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    3. Mingxin Xu, 2006. "Risk measure pricing and hedging in incomplete markets," Annals of Finance, Springer, vol. 2(1), pages 51-71, January.
    4. Riedel, Frank, 2010. "Optimal Stopping under Ambiguity," Center for Mathematical Economics Working Papers 390, Center for Mathematical Economics, Bielefeld University.
    5. Sabrina Mulinacci, 2011. "The efficient hedging problem for American options," Finance and Stochastics, Springer, vol. 15(2), pages 365-397, June.
    6. Karim El Moutaouakil & Abdellatif El Ouissari & Vasile Palade & Anas Charroud & Adrian Olaru & Hicham Baïzri & Saliha Chellak & Mouna Cheggour, 2023. "Multi-Objective Optimization for Controlling the Dynamics of the Diabetic Population," Mathematics, MDPI, vol. 11(13), pages 1-28, July.
    7. Alexander Chigodaev, 2016. "Recursive Method for Guaranteed Valuation of Options in Deterministic Game Theoretic Approach," HSE Working papers WP BRP 53/FE/2016, National Research University Higher School of Economics.
    8. 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.
    9. Hans Follmer & Alexander Schied, 2013. "Probabilistic aspects of finance," Papers 1309.7759, arXiv.org.
    10. Bruno Bouchard & Xiaolu Tan, 2021. "A quasi-sure optional decomposition and super-hedging result on the Skorokhod space," Finance and Stochastics, Springer, vol. 25(3), pages 505-528, July.
    11. Filipovic, Damir & Kupper, Michael, 2007. "Monotone and cash-invariant convex functions and hulls," Insurance: Mathematics and Economics, Elsevier, vol. 41(1), pages 1-16, July.
    12. Kohlmann, Michael & Niethammer, Christina R., 2007. "On convergence to the exponential utility problem," Stochastic Processes and their Applications, Elsevier, vol. 117(12), pages 1813-1834, December.
    13. Jun Sekine, 2012. "Long-term optimal portfolios with floor," Finance and Stochastics, Springer, vol. 16(3), pages 369-401, July.
    14. Joao Amaro de Matos & Ana Lacerda, 2004. "Dry markets and superreplication bounds of American derivatives," Nova SBE Working Paper Series wp461, Universidade Nova de Lisboa, Nova School of Business and Economics.

    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. Constantinos Kardaras, 2009. "No‐Free‐Lunch Equivalences For Exponential Lévy Models Under Convex Constraints On Investment," Mathematical Finance, Wiley Blackwell, vol. 19(2), pages 161-187, April.
    2. A. Fiori Maccioni, 2011. "The risk neutral valuation paradox," Working Paper CRENoS 201112, Centre for North South Economic Research, University of Cagliari and Sassari, Sardinia.
    3. F. Godin, 2016. "Minimizing CVaR in global dynamic hedging with transaction costs," Quantitative Finance, Taylor & Francis Journals, vol. 16(3), pages 461-475, March.
    4. Uwe Kuchler & Stefan Tappe, 2019. "Bilateral Gamma distributions and processes in financial mathematics," Papers 1907.09857, arXiv.org.
    5. Oliver X. Li & Weiping Li, 2015. "Hedging jump risk, expected returns and risk premia in jump-diffusion economies," Quantitative Finance, Taylor & Francis Journals, vol. 15(5), pages 873-888, May.
    6. Ole Barndorff-Nielsen & Elisa Nicolato & Neil Shephard, 2002. "Some recent developments in stochastic volatility modelling," Quantitative Finance, Taylor & Francis Journals, vol. 2(1), pages 11-23.
    7. Jan Bergenthum & Ludger Rüschendorf, 2006. "Comparison of Option Prices in Semimartingale Models," Finance and Stochastics, Springer, vol. 10(2), pages 222-249, April.
    8. feng dai, 2004. "The Partial Distribution: Definition, Properties and Applications in Economy," Econometrics 0403008, University Library of Munich, Germany.
    9. N. S. Gonchar, 2020. "Derivatives Pricing in Non-Arbitrage Market," Papers 2010.13630, arXiv.org.
    10. Ole Barndorff-Nielsen & Elisa Nicolato & Neil Shephard, 2002. "Some recent developments in stochastic volatility modelling," Quantitative Finance, Taylor & Francis Journals, vol. 2(1), pages 11-23.

    More about this item

    Keywords

    equivalent martingale measure; optional decomposition; semimartingale; Hellinger process; Lagrange multiplier;
    All these keywords.

    JEL classification:

    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

    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:zbw:sfb373:199754. 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: ZBW - Leibniz Information Centre for Economics (email available below). General contact details of provider: https://edirc.repec.org/data/sfhubde.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.