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On incompleteness of bond markets with infinite number of random factors

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  • Micha{l} Barski
  • Jacek Jakubowski
  • Jerzy Zabczyk

Abstract

The completeness of a bond market model with infinite number of sources of randomness on a finite time interval in the Heath-Jarrow-Morton framework is studied. It is proved that the market is not complete. A construction of a bounded contingent claim, which can not be replicated, is provided.

Suggested Citation

  • 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.
    • Handle: RePEc:arx:papers:0809.2270
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    References listed on IDEAS

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    1. Tomas Björk & Yuri Kabanov & Wolfgang Runggaldier, 1997. "Bond Market Structure in the Presence of Marked Point Processes," Mathematical Finance, Wiley Blackwell, vol. 7(2), pages 211-239, April.
    2. Jacek Jakubowski & Jerzy Zabczyk, 2007. "Exponential moments for HJM models with jumps," Finance and Stochastics, Springer, vol. 11(3), pages 429-445, July.
    3. Robert A. Jarrow & Dilip B. Madan, 1991. "A Characterization of Complete Security Markets On A Brownian Filtration1," Mathematical Finance, Wiley Blackwell, vol. 1(3), pages 31-43, July.
    4. Erik Taflin, 2005. "Bond market completeness and attainable contingent claims," Finance and Stochastics, Springer, vol. 9(3), pages 429-452, July.
    5. 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.
    6. Rene Carmona & Michael Tehranchi, 2004. "A Characterization of Hedging Portfolios for Interest Rate Contingent Claims," Papers math/0407119, arXiv.org.
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