IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v42y1999i1p27-31.html
   My bibliography  Save this article

A minimality property of the minimal martingale measure

Author

Listed:
  • Schweizer, Martin

Abstract

Let X be a continuous adapted process for which there exists an equivalent local martingale measure (ELMM). The minimal martingale measure is the unique ELMM for X with the property that local P-martingales strongly orthogonal to the P-martingale part of X are also local -martingales. We prove that if exists, it minimizes the reverse relative entropy H(PQ) over all ELMMs Q for X. A counterexample shows that the assumption of continuity cannot be dropped.

Suggested Citation

  • Schweizer, Martin, 1999. "A minimality property of the minimal martingale measure," Statistics & Probability Letters, Elsevier, vol. 42(1), pages 27-31, March.
    • Handle: RePEc:eee:stapro:v:42:y:1999:i:1:p:27-31
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(98)00180-1
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Norbert Hofmann & Eckhard Platen & Martin Schweizer, 1992. "Option Pricing Under Incompleteness and Stochastic Volatility," Mathematical Finance, Wiley Blackwell, vol. 2(3), pages 153-187, July.
    2. Martin Schweizer, 1995. "Variance-Optimal Hedging in Discrete Time," Mathematics of Operations Research, INFORMS, vol. 20(1), pages 1-32, February.
    3. Eckhard Platen & Rolando Rebolledo, 1996. "Principles for modelling financial markets," Published Paper Series 1996-3, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
    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. Weidong Tian & Daisuke Yoshikawa, 2017. "Analyzing Equilibrium in Incomplete Markets with Model Uncertainty," International Review of Finance, International Review of Finance Ltd., vol. 17(2), pages 235-262, June.
    2. Ioannis Karatzas & Constantinos Kardaras, 2007. "The numéraire portfolio in semimartingale financial models," Finance and Stochastics, Springer, vol. 11(4), pages 447-493, October.
    3. Fajardo, José & Corcuera, José Manuel & Menouken Pamen, Olivier, 2016. "On the optimal investment," MPRA Paper 71901, University Library of Munich, Germany.
    4. Vicky Henderson, 2002. "Analytical Comparisons of Option prices in Stochastic Volatility Models," OFRC Working Papers Series 2002mf03, Oxford Financial Research Centre.
    5. Ioannis Karatzas & Constantinos Kardaras, 2008. "The numeraire portfolio in semimartingale financial models," Papers 0803.1877, arXiv.org.
    6. Friedrich Hubalek & Carlo Sgarra, 2008. "On the Esscher transforms and other equivalent martingale measures for Barndorff-Nielsen and Shephard stochastic volatility models with jumps," Papers 0807.1227, arXiv.org.
    7. Thierry Chauveau & Hayette Gatfaoui, 2004. "Pricing and Hedging Options in Incomplete Markets: Idiosyncratic Risk, Systematic Risk and Stochastic Volatility," Research Paper Series 122, Quantitative Finance Research Centre, University of Technology, Sydney.
    8. Suleyman Basak & Georgy Chabakauri, 2010. "Dynamic Mean-Variance Asset Allocation," Review of Financial Studies, Society for Financial Studies, vol. 23(8), pages 2970-3016, August.
    9. Monoyios, Michael, 2007. "The minimal entropy measure and an Esscher transform in an incomplete market model," Statistics & Probability Letters, Elsevier, vol. 77(11), pages 1070-1076, June.
    10. Hubalek, Friedrich & Sgarra, Carlo, 2009. "On the Esscher transforms and other equivalent martingale measures for Barndorff-Nielsen and Shephard stochastic volatility models with jumps," Stochastic Processes and their Applications, Elsevier, vol. 119(7), pages 2137-2157, July.
    11. Vicky Henderson & David Hobson & Sam Howison & Tino Kluge, 2005. "A Comparison of Option Prices Under Different Pricing Measures in a Stochastic Volatility Model with Correlation," Review of Derivatives Research, Springer, vol. 8(1), pages 5-25, June.
    12. Stefan Kassberger & Thomas Liebmann, 2011. "Minimal q-entropy martingale measures for exponential time-changed Lévy processes," Finance and Stochastics, Springer, vol. 15(1), pages 117-140, January.
    13. Vicky Henderson & David Hobson & Sam Howison & Tino Kluge, 2003. "A Comparison of q-optimal Option Prices in a Stochastic Volatility Model with Correlation," OFRC Working Papers Series 2003mf02, Oxford Financial Research Centre.

    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. Eckhard Platen & Martin Schweizer, 1998. "On Feedback Effects from Hedging Derivatives," Mathematical Finance, Wiley Blackwell, vol. 8(1), pages 67-84, January.
    2. Sergei Fedotov & Sergei Mikhailov, 2001. "Option Pricing For Incomplete Markets Via Stochastic Optimization: Transaction Costs, Adaptive Control And Forecast," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 4(01), pages 179-195.
    3. Sergei Fedotov & Sergei Mikhailov, 1998. "Option Pricing Model for Incomplete Market," Papers cond-mat/9807397, arXiv.org, revised Aug 1998.
    4. Aleš Černý, 2007. "Optimal Continuous‐Time Hedging With Leptokurtic Returns," Mathematical Finance, Wiley Blackwell, vol. 17(2), pages 175-203, April.
    5. Bjork, Tomas, 2009. "Arbitrage Theory in Continuous Time," OUP Catalogue, Oxford University Press, edition 3, number 9780199574742, Decembrie.
    6. Bekker, Paul A., 2004. "A mean-variance frontier in discrete and continuous time," CCSO Working Papers 200406, University of Groningen, CCSO Centre for Economic Research.
    7. Eckhard Platen, 2003. "Pricing and Hedging for Incomplete Jump Diffusion Benchmark Models," Research Paper Series 110, Quantitative Finance Research Centre, University of Technology, Sydney.
    8. David Heath & Eckhard Platen, 2002. "A variance reduction technique based on integral representations," Quantitative Finance, Taylor & Francis Journals, vol. 2(5), pages 362-369.
    9. Huyên Pham, 2003. "A large deviations approach to optimal long term investment," Finance and Stochastics, Springer, vol. 7(2), pages 169-195.
    10. Alexandre Carbonneau & Fr'ed'eric Godin, 2021. "Deep equal risk pricing of financial derivatives with non-translation invariant risk measures," Papers 2107.11340, arXiv.org.
    11. F. Fornari & A. Mele, 1998. "ARCH Models and Option Pricing : The Continuous Time Connection," THEMA Working Papers 98-30, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    12. Chenxu Li, 2016. "Bessel Processes, Stochastic Volatility, And Timer Options," Mathematical Finance, Wiley Blackwell, vol. 26(1), pages 122-148, January.
    13. Gatfaoui Hayette, 2004. "Idiosyncratic Risk, Systematic Risk and Stochastic Volatility: An Implementation of Merton’s Credit Risk Valuation," Finance 0404004, University Library of Munich, Germany.
    14. Kolkiewicz, A. W. & Tan, K. S., 2006. "Unit-Linked Life Insurance Contracts with Lapse Rates Dependent on Economic Factors," Annals of Actuarial Science, Cambridge University Press, vol. 1(1), pages 49-78, March.
    15. Augustyniak, Maciej & Godin, Frédéric & Simard, Clarence, 2019. "A profitable modification to global quadratic hedging," Journal of Economic Dynamics and Control, Elsevier, vol. 104(C), pages 111-131.
    16. Panagiotis Christodoulou & Nils Detering & Thilo Meyer-Brandis, 2018. "Local Risk-Minimization With Multiple Assets Under Illiquidity With Applications In Energy Markets," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(04), pages 1-44, June.
    17. Schweizer, Martin, 2001. "From actuarial to financial valuation principles," Insurance: Mathematics and Economics, Elsevier, vol. 28(1), pages 31-47, February.
    18. Silvia Florio & Wolfgang Runggaldier, 1999. "On hedging in finite security markets," Applied Mathematical Finance, Taylor & Francis Journals, vol. 6(3), pages 159-176.
    19. Robert A. Jarrow, 2008. "Derivative Security Markets, Market Manipulation, and Option Pricing Theory," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 7, pages 131-151, World Scientific Publishing Co. Pte. Ltd..
    20. Platen, Eckhard, 1995. "On weak implicit and predictor-corrector methods," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 38(1), pages 69-76.

    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:eee:stapro:v:42:y:1999:i:1:p:27-31. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.