IDEAS home Printed from https://ideas.repec.org/a/spr/finsto/v27y2023i2d10.1007_s00780-023-00503-3.html
   My bibliography  Save this article

Optional projection under equivalent local martingale measures

Author

Listed:
  • Francesca Biagini

    (Ludwig-Maximilians Universität)

  • Andrea Mazzon

    (Ludwig-Maximilians Universität)

  • Ari-Pekka Perkkiö

    (Ludwig-Maximilians Universität)

Abstract

We study optional projections of G ${\mathbb{G}}$ -adapted strict local martingales on a smaller filtration F ${\mathbb{F}}$ under changes of equivalent martingale measures. General results are provided as well as a detailed analysis of two specific examples given by the inverse Bessel process and a class of stochastic volatility models. This analysis contributes to clarify the absence of arbitrage opportunities of market models under restricted information.

Suggested Citation

  • Francesca Biagini & Andrea Mazzon & Ari-Pekka Perkkiö, 2023. "Optional projection under equivalent local martingale measures," Finance and Stochastics, Springer, vol. 27(2), pages 435-465, April.
    • Handle: RePEc:spr:finsto:v:27:y:2023:i:2:d:10.1007_s00780-023-00503-3
    DOI: 10.1007/s00780-023-00503-3
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00780-023-00503-3
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00780-023-00503-3?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    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. Umut Çetin & Robert Jarrow & Philip Protter & Yildiray Yildirim, 2008. "Modeling Credit Risk With Partial Information," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 23, pages 579-590, World Scientific Publishing Co. Pte. Ltd..
    2. Dolinsky, Yan & Zouari, Jonathan, 2020. "Market delay and G-expectations," Stochastic Processes and their Applications, Elsevier, vol. 130(2), pages 694-707.
    3. Wolfgang J. Runggaldier & Anna Zaccaria, 2000. "A Stochastic Control Approach to Risk Management Under Restricted Information," Mathematical Finance, Wiley Blackwell, vol. 10(2), pages 277-288, April.
    4. Rüdiger Frey & Wolfgang J. Runggaldier, 1999. "Risk-minimizing hedging strategies under restricted information: The case of stochastic volatility models observable only at discrete random times," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 50(2), pages 339-350, October.
    5. Caroline Hillairet & Ying Jiao, 2012. "Credit Risk with asymmetric information on the default threshold," Post-Print hal-00663136, HAL.
    6. Robert A. Jarrow, 2009. "Credit Risk Models," Annual Review of Financial Economics, Annual Reviews, vol. 1(1), pages 37-68, November.
    7. Peter Bank & Yan Dolinsky, 2020. "A Note on Utility Indifference Pricing with Delayed Information," Papers 2011.05023, arXiv.org, revised Mar 2021.
    8. Robert Jarrow & Philip Protter & A. Sezer, 2007. "Information reduction via level crossings in a credit risk model," Finance and Stochastics, Springer, vol. 11(2), pages 195-212, April.
    9. Kardaras, Constantinos & Ruf, Johannes, 2019. "Projections of scaled bessel processes," LSE Research Online Documents on Economics 100939, London School of Economics and Political Science, LSE Library.
    10. Giorgia Callegaro & Monique Jeanblanc & Wolfgang Runggaldier, 2012. "Portfolio optimization in a defaultable market under incomplete information," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 35(2), pages 91-111, November.
    11. Constantinos Kardaras & Johannes Ruf, 2020. "Filtration shrinkage, the structure of deflators, and failure of market completeness," Finance and Stochastics, Springer, vol. 24(4), pages 871-901, October.
    12. Freddy Delbaen & Walter Schachermayer, 1994. "Arbitrage And Free Lunch With Bounded Risk For Unbounded Continuous Processes," Mathematical Finance, Wiley Blackwell, vol. 4(4), pages 343-348, October.
    13. Xin Guo & Robert A. Jarrow & Yan Zeng, 2009. "Credit Risk Models with Incomplete Information," Mathematics of Operations Research, INFORMS, vol. 34(2), pages 320-332, May.
    14. Constantinos Kardaras & Johannes Ruf, 2019. "Filtration shrinkage, the structure of deflators, and failure of market completeness," Papers 1912.04652, arXiv.org, revised Aug 2020.
    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. Junchi Ma & Mobolaji Ogunsolu & Jinniao Qiu & Ayşe Deniz Sezer, 2023. "Credit risk pricing in a consumption‐based equilibrium framework with incomplete accounting information," Mathematical Finance, Wiley Blackwell, vol. 33(3), pages 666-708, July.
    2. Umut Cetin & Kasper Larsen, 2020. "Uniqueness in Cauchy problems for diffusive real-valued strict local martingales," Papers 2007.15041, arXiv.org, revised May 2022.
    3. Francesca Biagini & Andrea Mazzon & Ari-Pekka Perkkio, 2020. "Optional projection under equivalent local martingale measures," Papers 2003.09940, arXiv.org.
    4. Dong, Xin & Zheng, Harry, 2015. "Intensity process for a pure jump Lévy structural model with incomplete information," Stochastic Processes and their Applications, Elsevier, vol. 125(4), pages 1307-1322.
    5. Çetin, Umut & Larsen, Kasper, 2023. "Uniqueness in cauchy problems for diffusive real-valued strict local martingales," LSE Research Online Documents on Economics 118743, London School of Economics and Political Science, LSE Library.
    6. Xin Dong & Harry Zheng, 2014. "Intensity Process for a Pure Jump L\'evy Structural Model with Incomplete Information," Papers 1405.3767, arXiv.org.
    7. Juan Dong & Lyudmila Korobenko & Deniz Sezer, 2019. "Nonhedgeable risk and Credit Risk Pricing," Papers 1910.08641, arXiv.org.
    8. Jose Giancarlo Gasha & Mr. Andre O Santos & Mr. Jorge A Chan-Lau & Mr. Carlos I. Medeiros & Mr. Marcos R Souto & Christian Capuano, 2009. "Recent Advances in Credit Risk Modeling," IMF Working Papers 2009/162, International Monetary Fund.
    9. Robert Jarrow & Philip Protter, 2020. "Credit Risk, Liquidity, and Bubbles," International Review of Finance, International Review of Finance Ltd., vol. 20(3), pages 737-746, September.
    10. Caroline Hillairet & Ying Jiao, 2012. "Credit Risk with asymmetric information on the default threshold," Post-Print hal-00663136, HAL.
    11. Černý, Aleš & Ruf, Johannes, 2023. "Simplified calculus for semimartingales: Multiplicative compensators and changes of measure," Stochastic Processes and their Applications, Elsevier, vol. 161(C), pages 572-602.
    12. Lindset, Snorre & Lund, Arne-Christian & Persson, Svein-Arne, 2014. "Credit risk and asymmetric information: A simplified approach," Journal of Economic Dynamics and Control, Elsevier, vol. 39(C), pages 98-112.
    13. Çetin, Umut, 2012. "On absolutely continuous compensators and nonlinear filtering equations in default risk models," Stochastic Processes and their Applications, Elsevier, vol. 122(11), pages 3619-3647.
    14. Lijun Bo & Yongjin Wang & Xuewei Yang, 2014. "On the Default Probability in a Regime-Switching Regulated Market," Methodology and Computing in Applied Probability, Springer, vol. 16(1), pages 101-113, March.
    15. Delia Coculescu & Monique Jeanblanc & Ashkan Nikeghbali, 2012. "Default times, no-arbitrage conditions and changes of probability measures," Finance and Stochastics, Springer, vol. 16(3), pages 513-535, July.
    16. Nicole El Karoui & Monique Jeanblanc & Ying Jiao, 2017. "Dynamics of multivariate default system in random environment," Post-Print hal-01205753, HAL.
    17. Tim Leung & Michael Ludkovski, 2010. "Optimal Timing to Purchase Options," Papers 1008.3650, arXiv.org, revised Apr 2011.
    18. Xu, Xin, 2013. "Forecasting Bankruptcy with Incomplete Information," MPRA Paper 55024, University Library of Munich, Germany, revised 31 Mar 2014.
    19. El Karoui, Nicole & Jeanblanc, Monique & Jiao, Ying, 2017. "Dynamics of multivariate default system in random environment," Stochastic Processes and their Applications, Elsevier, vol. 127(12), pages 3943-3965.
    20. Jos'e Manuel Corcuera & Arturo Valdivia, 2016. "CoCos under short-term uncertainty," Papers 1602.00094, arXiv.org.

    More about this item

    Keywords

    Local martingale; Optional projection; Local martingale measure; Filtration shrinkage;
    All these keywords.

    JEL classification:

    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

    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:spr:finsto:v:27:y:2023:i:2:d:10.1007_s00780-023-00503-3. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.