IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v46y2000i1p43-51.html
   My bibliography  Save this article

On Novikov and arbitrage properties of multidimensional diffusion processes with exploding drift

Author

Listed:
  • Stummer, Wolfgang

Abstract

We investigate properties of processes Xt which are weak solutions of multidimensional stochastic differential equations of the formdXt=b(t,Xt) dt+dWt.We show that under certain non-stochastic conditions the solution Xt itself satisfies a uniform Novikov property. Consequently, it will follow that under these assumptions the no arbitrage property of Xt can be obtained by applying the Girsanov theorem twice (in reverse directions). For the sake of illustration, some examples with exploding drifts b are presented.

Suggested Citation

  • Stummer, Wolfgang, 2000. "On Novikov and arbitrage properties of multidimensional diffusion processes with exploding drift," Statistics & Probability Letters, Elsevier, vol. 46(1), pages 43-51, January.
    • Handle: RePEc:eee:stapro:v:46:y:2000:i:1:p:43-51
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(99)00085-1
    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. Freddy Delbaen, 1992. "Representing Martingale Measures When Asset Prices Are Continuous And Bounded," Mathematical Finance, Wiley Blackwell, vol. 2(2), pages 107-130, April.
    2. Stummer, Wolfgang, 1998. "On bounded entropy of solutions of multi-dimensional stochastic differential equations," Statistics & Probability Letters, Elsevier, vol. 36(4), pages 327-336, January.
    3. Stummer, Wolfgang, 1997. "On exponential moments of two Brownian functionals," Statistics & Probability Letters, Elsevier, vol. 31(3), pages 233-237, January.
    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. Rogers, L. C. G. & Stummer, Wolfgang, 2000. "Consistent fitting of one-factor models to interest rate data," Insurance: Mathematics and Economics, Elsevier, vol. 27(1), pages 45-63, August.

    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. Bjork, Tomas, 2009. "Arbitrage Theory in Continuous Time," OUP Catalogue, Oxford University Press, edition 3, number 9780199574742.
    2. Beißner, Patrick, 2013. "Coherent Price Systems and Uncertainty-Neutral Valuation," VfS Annual Conference 2013 (Duesseldorf): Competition Policy and Regulation in a Global Economic Order 80010, Verein für Socialpolitik / German Economic Association.
    3. Alessandro Fiori Maccioni, 2011. "Endogenous Bubbles in Derivatives Markets: The Risk Neutral Valuation Paradox," Papers 1106.5274, arXiv.org, revised Sep 2011.
    4. repec:dau:papers:123456789/5374 is not listed on IDEAS
    5. Gabriel Frahm, 2013. "Pricing and Valuation under the Real-World Measure," Papers 1304.3824, arXiv.org, revised Jan 2016.
    6. Jouini, Elyes, 2001. "Arbitrage and control problems in finance: A presentation," Journal of Mathematical Economics, Elsevier, vol. 35(2), pages 167-183, April.
    7. Napp, Clotilde, 2001. "Pricing issues with investment flows Applications to market models with frictions," Journal of Mathematical Economics, Elsevier, vol. 35(3), pages 383-408, June.
    8. Frittelli, Marco, 1996. "Dominated families of martingale, supermartingale and quasimartingale laws," Stochastic Processes and their Applications, Elsevier, vol. 63(2), pages 265-277, November.
    9. Stephen A. Clark, 2003. "An Infinite-Dimensional LP Duality Theorem," Mathematics of Operations Research, INFORMS, vol. 28(2), pages 233-245, May.
    10. Christa Cuchiero & Josef Teichmann, 2014. "A convergence result for the Emery topology and a variant of the proof of the fundamental theorem of asset pricing," Papers 1406.5414, arXiv.org, revised Jul 2014.
    11. Rüdiger Frey & Carlos A. Sin, 1999. "Bounds on European Option Prices under Stochastic Volatility," Mathematical Finance, Wiley Blackwell, vol. 9(2), pages 97-116, April.
    12. Elyès Jouini, 2003. "Market imperfections , equilibrium and arbitrage," Post-Print halshs-00167131, HAL.
    13. D'Auria, Bernardo & Salmerón Garrido, José Antonio, 2019. "Insider information and its relation with the arbitrage condition and the utility maximization problem," DES - Working Papers. Statistics and Econometrics. WS 28805, Universidad Carlos III de Madrid. Departamento de Estadística.
    14. Dean Buckner & Kevin Dowd & Hardy Hulley, 2022. "Arbitrage Problems with Reflected Geometric Brownian Motion," Papers 2201.05312, arXiv.org, revised Sep 2022.
    15. Christa Cuchiero & Josef Teichmann, 2015. "A convergence result for the Emery topology and a variant of the proof of the fundamental theorem of asset pricing," Finance and Stochastics, Springer, vol. 19(4), pages 743-761, October.
    16. Hardy Hulley, 2009. "Strict Local Martingales in Continuous Financial Market Models," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 19, July-Dece.
    17. Hardy Hulley, 2009. "Strict Local Martingales in Continuous Financial Market Models," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 2-2009, January-A.
    18. 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.
    19. Patrick Bei{ss}ner, 2012. "Coherent Price Systems and Uncertainty-Neutral Valuation," Papers 1202.6632, arXiv.org.
    20. Jaime A. Londo~no, 2003. "State Tameness: A New Approach for Credit Constrains," Papers math/0305274, arXiv.org, revised Feb 2004.
    21. repec:dau:papers:123456789/12663 is not listed on IDEAS
    22. Nietert, Bernhard & Wilhelm, Jochen, 2001. "Some economic remarks on arbitrage theory," Passauer Diskussionspapiere, Betriebswirtschaftliche Reihe 7, University of Passau, Faculty of Business and Economics.

    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:46:y:2000:i:1:p:43-51. 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.