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A theory of stochastic integration for bond markets

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  • 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
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    References listed on IDEAS

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    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. 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..
    3. 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.
    4. Rene Carmona & Michael Tehranchi, 2004. "A Characterization of Hedging Portfolios for Interest Rate Contingent Claims," Papers math/0407119, arXiv.org.
    5. 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.
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    Cited by:

    1. Constantinos Kardaras, 2011. "On the closure in the Emery topology of semimartingale wealth-process sets," Papers 1108.0945, arXiv.org, revised Jul 2013.
    2. 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.
    3. Claudio Fontana & Thorsten Schmidt, 2016. "General dynamic term structures under default risk," Papers 1603.03198, arXiv.org, revised Nov 2017.
    4. 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.
    5. 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.
    6. 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.
    7. Yushi Hamaguchi, 2018. "BSDEs driven by cylindrical martingales with application to approximate hedging in bond markets," Papers 1806.04025, arXiv.org.
    8. Scott Robertson & Konstantinos Spiliopoulos, 2014. "Indifference pricing for Contingent Claims: Large Deviations Effects," Papers 1410.0384, arXiv.org, revised Feb 2016.
    9. 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.
    10. Alberto Ohashi, 2008. "Fractional term structure models: No-arbitrage and consistency," Papers 0802.1288, arXiv.org, revised Sep 2009.

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