IDEAS home Printed from https://ideas.repec.org/p/arx/papers/math-0602532.html
   My bibliography  Save this paper

A theory of stochastic integration for bond markets

Author

Listed:
  • M. De Donno
  • M. Pratelli

Abstract

We introduce a theory of stochastic integration with respect to a family of semimartingales depending on a continuous parameter, as a mathematical background to the theory of bond markets. We apply our results to the problem of super-replication and utility maximization from terminal wealth in a bond market. Finally, we compare our approach to those already existing in literature.

Suggested Citation

  • M. De Donno & M. Pratelli, 2006. "A theory of stochastic integration for bond markets," Papers math/0602532, arXiv.org.
  • Handle: RePEc:arx:papers:math/0602532
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/math/0602532
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Marzia Donno & Maurizio Pratelli, 2004. "On the use of measure-valued strategies in bond markets," Finance and Stochastics, Springer, vol. 8(1), pages 87-109, January.
    2. Unknown, 2005. "Forward," 2005 Conference: Slovenia in the EU - Challenges for Agriculture, Food Science and Rural Affairs, November 10-11, 2005, Moravske Toplice, Slovenia 183804, Slovenian Association of Agricultural Economists (DAES).
    3. Marzia De Donno, 2004. "The Term Structure of Interest Rates as a Random Field: a Stochastic Integration Approach," World Scientific Book Chapters, in: Jiro Akahori & Shigeyoshi Ogawa & Shinzo Watanabe (ed.), Stochastic Processes And Applications To Mathematical Finance, chapter 2, pages 27-52, World Scientific Publishing Co. Pte. Ltd..
    4. Shin Ichi Aihara & Arunabha Bagchi, 2005. "Stochastic Hyperbolic Dynamics For Infinite‐Dimensional Forward Rates And Option Pricing," Mathematical Finance, Wiley Blackwell, vol. 15(1), pages 27-47, January.
    5. Rene Carmona & Michael Tehranchi, 2004. "A Characterization of Hedging Portfolios for Interest Rate Contingent Claims," Papers math/0407119, arXiv.org.
    6. De Donno, M. & Guasoni, P. & Pratelli, M., 2005. "Super-replication and utility maximization in large financial markets," Stochastic Processes and their Applications, Elsevier, vol. 115(12), pages 2006-2022, December.
    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. Bruno Bouchard & Erik Taflin, 2010. "No-arbitrage of second kind in countable markets with proportional transaction costs," Papers 1008.3276, arXiv.org, revised Feb 2013.
    2. Kardaras, Constantinos, 2013. "On the closure in the Emery topology of semimartingale wealth-process sets," LSE Research Online Documents on Economics 44996, London School of Economics and Political Science, LSE Library.
    3. Yushi Hamaguchi, 2018. "BSDEs driven by cylindrical martingales with application to approximate hedging in bond markets," Papers 1806.04025, arXiv.org.
    4. Constantinos Kardaras, 2011. "On the closure in the Emery topology of semimartingale wealth-process sets," Papers 1108.0945, arXiv.org, revised Jul 2013.
    5. Scott Robertson & Konstantinos Spiliopoulos, 2014. "Indifference pricing for Contingent Claims: Large Deviations Effects," Papers 1410.0384, arXiv.org, revised Feb 2016.
    6. Thorsten Schmidt, 2006. "An Infinite Factor Model For Credit Risk," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 9(01), pages 43-68.
    7. Kühn, Christoph & Stroh, Maximilian, 2013. "Continuous time trading of a small investor in a limit order market," Stochastic Processes and their Applications, Elsevier, vol. 123(6), pages 2011-2053.
    8. Claudio Fontana & Thorsten Schmidt, 2016. "General dynamic term structures under default risk," Papers 1603.03198, arXiv.org, revised Nov 2017.
    9. Alberto Ohashi, 2008. "Fractional term structure models: No-arbitrage and consistency," Papers 0802.1288, arXiv.org, revised Sep 2009.
    10. Claudio Fontana & Zorana Grbac & Sandrine Gumbel & Thorsten Schmidt, 2018. "Term structure modeling for multiple curves with stochastic discontinuities," Papers 1810.09882, arXiv.org, revised Dec 2019.

    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. Micha{l} Barski & Jacek Jakubowski & Jerzy Zabczyk, 2008. "On incompleteness of bond markets with infinite number of random factors," Papers 0809.2270, arXiv.org, revised Jan 2016.
    2. Oleksii Mostovyi, 2014. "Utility maximization in the large markets," Papers 1403.6175, arXiv.org, revised Oct 2014.
    3. Roncoroni, Andrea & Galluccio, Stefano & Guiotto, Paolo, 2010. "Shape factors and cross-sectional risk," Journal of Economic Dynamics and Control, Elsevier, vol. 34(11), pages 2320-2340, November.
    4. Yushi Hamaguchi, 2018. "BSDEs driven by cylindrical martingales with application to approximate hedging in bond markets," Papers 1806.04025, arXiv.org.
    5. Erik Taflin, 2009. "Generalized integrands and bond portfolios: Pitfalls and counter examples," Papers 0909.2341, arXiv.org, revised Jan 2011.
    6. Pilar Lopez-Llompart & G. Mathias Kondolf, 2016. "Encroachments in floodways of the Mississippi River and Tributaries Project," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 81(1), pages 513-542, March.
    7. Cheng, Jianquan & Bertolini, Luca, 2013. "Measuring urban job accessibility with distance decay, competition and diversity," Journal of Transport Geography, Elsevier, vol. 30(C), pages 100-109.
    8. Prilly Oktoviany & Robert Knobloch & Ralf Korn, 2021. "A machine learning-based price state prediction model for agricultural commodities using external factors," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 44(2), pages 1063-1085, December.
    9. Michelle Sheran Sylvester, 2007. "The Career and Family Choices of Women: A Dynamic Analysis of Labor Force Participation, Schooling, Marriage and Fertility Decisions," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 10(3), pages 367-399, July.
    10. Henrekson, Magnus & Johansson, Dan, 2010. "Firm Growth, Institutions and Structural Transformation," Ratio Working Papers 150, The Ratio Institute.
    11. Karen K. Lewis, 2011. "Global Asset Pricing," Annual Review of Financial Economics, Annual Reviews, vol. 3(1), pages 435-466, December.
    12. DAVID M. BLAU & WILBERT van der KLAAUW, 2013. "What Determines Family Structure?," Economic Inquiry, Western Economic Association International, vol. 51(1), pages 579-604, January.
    13. Panagiota DIONYSOPOULOU & Georgios SVARNIAS & Theodore PAPAILIAS, 2021. "Total Quality Management In Public Sector, Case Study: Customs Service," Regional Science Inquiry, Hellenic Association of Regional Scientists, vol. 0(1), pages 153-168, June.
    14. Afanasyev, Dmitriy O. & Fedorova, Elena A. & Popov, Viktor U., 2015. "Fine structure of the price–demand relationship in the electricity market: Multi-scale correlation analysis," Energy Economics, Elsevier, vol. 51(C), pages 215-226.
    15. Peter Viggo Jakobsen, 2009. "Small States, Big Influence: The Overlooked Nordic Influence on the Civilian ESDP," Journal of Common Market Studies, Wiley Blackwell, vol. 47(1), pages 81-102, January.
    16. Julie Holland Mortimer, 2007. "Price Discrimination, Copyright Law, and Technological Innovation: Evidence from the Introduction of DVDs," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 122(3), pages 1307-1350.
    17. Suwan Shen & Xi Feng & Zhong Ren Peng, 2016. "A framework to analyze vulnerability of critical infrastructure to climate change: the case of a coastal community in Florida," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 84(1), pages 589-609, October.
    18. Jean-Bernard Chatelain & Kirsten Ralf, 2017. "Can We Identify the Fed's Preferences?," Working Papers halshs-01549908, HAL.
    19. Billio, Monica & Casarin, Roberto & Osuntuyi, Anthony, 2016. "Efficient Gibbs sampling for Markov switching GARCH models," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 37-57.
    20. Jan Babecký & Fabrizio Coricelli & Roman Horváth, 2009. "Assessing Inflation Persistence: Micro Evidence on an Inflation Targeting Economy," Czech Journal of Economics and Finance (Finance a uver), Charles University Prague, Faculty of Social Sciences, vol. 59(2), pages 102-127, June.

    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:math/0602532. 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.