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On the use of measure-valued strategies in bond markets

Author

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  • Marzia Donno
  • Maurizio Pratelli

Abstract

We propose here a theory of cylindrical stochastic integration, recently developed by Mikulevicius and Rozovskii, as mathematical background to the theory of bond markets. In this theory, since there is a continuum of securities, it seems natural to define a portfolio as a measure on maturities. However, it turns out that this set of strategies is not complete, and the theory of cylindrical integration allows one to overcome this difficulty. Our approach generalizes the measure-valued strategies: this explains some known results, such as approximate completeness, but at the same time it also shows that either the optimal strategy is based on a finite number of bonds or it is not necessarily a measure-valued process. Copyright Springer-Verlag Berlin/Heidelberg 2004

Suggested Citation

  • 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.
    • Handle: RePEc:spr:finsto:v:8:y:2004:i:1:p:87-109
    DOI: 10.1007/s00780-003-0102-7
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    Citations

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    Cited by:

    1. M. De Donno & M. Pratelli, 2006. "A theory of stochastic integration for bond markets," Papers math/0602532, arXiv.org.
    2. Yushi Hamaguchi, 2018. "BSDEs driven by cylindrical martingales with application to approximate hedging in bond markets," Papers 1806.04025, arXiv.org.
    3. Rene Carmona & Michael Tehranchi, 2004. "A Characterization of Hedging Portfolios for Interest Rate Contingent Claims," Papers math/0407119, arXiv.org.
    4. repec:dau:papers:123456789/12663 is not listed on IDEAS
    5. Oleksii Mostovyi, 2014. "Utility maximization in the large markets," Papers 1403.6175, arXiv.org, revised Oct 2014.
    6. Erik Taflin, 2009. "Generalized integrands and bond portfolios: Pitfalls and counter examples," Papers 0909.2341, arXiv.org, revised Jan 2011.

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