IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1403.3459.html
   My bibliography  Save this paper

Structure conditions under progressively added information

Author

Listed:
  • Tahir Choulli
  • Jun Deng

Abstract

It has been understood that the "local" existence of the Markowitz' optimal portfolio or the solution to the local-risk minimization problem is guaranteed by some specific mathematical structures on the underlying assets price processes known in the literature as "{\it Structure Conditions}". In this paper, we consider a semi-martingale market model, and an arbitrary random time that is not adapted to the information flow of the market model. This random time may model the default time of a firm, the death time of an insured, or any the occurrence time of an event that might impact the market model somehow. By adding additional uncertainty to the market model, via this random time, the {\it structures conditions} may fail and hence the Markowitz's optimal portfolio and other quadratic-optimal portfolios might fail to exist. Our aim is to investigate the impact of this random time on the structures conditions from different perspectives. Our analysis allows us to conclude that under some mild assumptions on the market model and the random time, these structures conditions will remain valid on the one hand. Furthermore, we provide two examples illustrating the importance of these assumptions. On the other hand, we describe the random time models for which these structure conditions are preserved for any market model. These results are elaborated separately for the two contexts of stopping with the random time and incorporating totally a specific class of random times respectively.

Suggested Citation

  • Tahir Choulli & Jun Deng, 2014. "Structure conditions under progressively added information," Papers 1403.3459, arXiv.org, revised Dec 2018.
    • Handle: RePEc:arx:papers:1403.3459
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1403.3459
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Alev{s} v{C}ern'y & Jan Kallsen, 2007. "On the Structure of General Mean-Variance Hedging Strategies," Papers 0708.1715, arXiv.org, revised Jul 2017.
    2. Amendinger, Jürgen & Imkeller, Peter & Schweizer, Martin, 1998. "Additional logarithmic utility of an insider," Stochastic Processes and their Applications, Elsevier, vol. 75(2), pages 263-286, July.
    3. Arturo Kohatsu‐Higa & Agnès Sulem, 2006. "Utility Maximization In An Insider Influenced Market," Mathematical Finance, Wiley Blackwell, vol. 16(1), pages 153-179, January.
    4. Jean-Paul Laurent & Huyen Pham, 1999. "Dynamic programming and mean-variance hedging," Post-Print hal-03675953, HAL.
    5. Allen, Beth, 1990. "Information as an Economic Commodity," American Economic Review, American Economic Association, vol. 80(2), pages 268-273, May.
    6. Francesca Biagini & Paolo Guasoni & Maurizio Pratelli, 2000. "Mean‐Variance Hedging for Stochastic Volatility Models," Mathematical Finance, Wiley Blackwell, vol. 10(2), pages 109-123, April.
    7. Schweizer, Martin, 1999. "A guided tour through quadratic hedging approaches," SFB 373 Discussion Papers 1999,96, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    8. Chichilnisky,Graciela (ed.), 1999. "Markets, Information and Uncertainty," Cambridge Books, Cambridge University Press, number 9780521553551.
    9. David Heath & Eckhard Platen & Martin Schweizer, 2001. "A Comparison of Two Quadratic Approaches to Hedging in Incomplete Markets," Mathematical Finance, Wiley Blackwell, vol. 11(4), pages 385-413, October.
    10. Amendinger, Jürgen & Imkeller, Peter & Schweizer, Martin, 1998. "Additional logarithmic utility of an insider," SFB 373 Discussion Papers 1998,25, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    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. Tahir Choulli & Sina Yansori, 2018. "Log-optimal portfolio and num\'eraire portfolio for market models stopped at a random time," Papers 1810.12762, arXiv.org, revised Aug 2020.
    2. Tahir Choulli & Sina Yansori, 2018. "Explicit description of all deflators for market models under random horizon with applications to NFLVR," Papers 1803.10128, arXiv.org, revised Feb 2021.

    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. Bernardo D'Auria & Jos'e Antonio Salmer'on, 2017. "Valuing the anticipative information on the stochastic short interest rates," Papers 1711.03642, arXiv.org, revised Nov 2021.
    2. Tahir Choulli & Sina Yansori, 2018. "Explicit description of all deflators for market models under random horizon with applications to NFLVR," Papers 1803.10128, arXiv.org, revised Feb 2021.
    3. Tahir Choulli & Sina Yansori, 2022. "Log-optimal and numéraire portfolios for market models stopped at a random time," Finance and Stochastics, Springer, vol. 26(3), pages 535-585, July.
    4. Tahir Choulli & Sina Yansori, 2018. "Log-optimal portfolio and num\'eraire portfolio for market models stopped at a random time," Papers 1810.12762, arXiv.org, revised Aug 2020.
    5. Wanyang Dai, 2014. "Mean-variance hedging based on an incomplete market with external risk factors of non-Gaussian OU processes," Papers 1410.0991, arXiv.org, revised Aug 2015.
    6. Kohatsu-Higa, Arturo & Yamazato, Makoto, 2008. "Enlargement of filtrations with random times for processes with jumps," Stochastic Processes and their Applications, Elsevier, vol. 118(7), pages 1136-1158, July.
    7. Huy N. Chau & Andrea Cosso & Claudio Fontana, 2018. "The value of informational arbitrage," Papers 1804.00442, arXiv.org.
    8. Anna Aksamit & Tahir Choulli & Jun Deng & Monique Jeanblanc, 2015. "Non-Arbitrage Under Additional Information for Thin Semimartingale Models," Papers 1505.00997, arXiv.org.
    9. Thorsten Rheinländer, 2005. "An entropy approach to the Stein and Stein model with correlation," Finance and Stochastics, Springer, vol. 9(3), pages 399-413, July.
    10. D'Auria, Bernardo & García Martí, Dolores & Salmerón Garrido, José Antonio, 2017. "Optimal portfolio with insider information on the stochastic interest rate," DES - Working Papers. Statistics and Econometrics. WS 25819, Universidad Carlos III de Madrid. Departamento de Estadística.
    11. Anna Aksamit & Tahir Choulli & Jun Deng & Monique Jeanblanc, 2017. "No-arbitrage up to random horizon for quasi-left-continuous models," Finance and Stochastics, Springer, vol. 21(4), pages 1103-1139, October.
    12. Francesca Biagini & Paolo Guasoni & Maurizio Pratelli, 2000. "Mean‐Variance Hedging for Stochastic Volatility Models," Mathematical Finance, Wiley Blackwell, vol. 10(2), pages 109-123, April.
    13. David Hobson, 2004. "STOCHASTIC VOLATILITY MODELS, CORRELATION, AND THE q‐OPTIMAL MEASURE," Mathematical Finance, Wiley Blackwell, vol. 14(4), pages 537-556, October.
    14. Aksamit, Anna & Choulli, Tahir & Deng, Jun & Jeanblanc, Monique, 2019. "No-arbitrage under additional information for thin semimartingale models," Stochastic Processes and their Applications, Elsevier, vol. 129(9), pages 3080-3115.
    15. Aleš Černý, 2007. "Optimal Continuous‐Time Hedging With Leptokurtic Returns," Mathematical Finance, Wiley Blackwell, vol. 17(2), pages 175-203, April.
    16. Michael Mania & Revaz Tevzadze, 2008. "Backward Stochastic PDEs Related to the Utility Maximization Problem," ICER Working Papers - Applied Mathematics Series 07-2008, ICER - International Centre for Economic Research.
    17. 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.
    18. 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.
    19. Ernst, Philip A. & Rogers, L.C.G. & Zhou, Quan, 2017. "The value of foresight," Stochastic Processes and their Applications, Elsevier, vol. 127(12), pages 3913-3927.
    20. Beatrice Acciaio & Claudio Fontana & Constantinos Kardaras, 2014. "Arbitrage of the first kind and filtration enlargements in semimartingale financial models," Papers 1401.7198, arXiv.org, revised May 2015.

    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:1403.3459. 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.