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Incompleteness of the bond market with Lévy noise under the physical measure

Volume 104 / 2015

Michał Barski Banach Center Publications 104 (2015), 61-84 MSC: 91B26, 91B70. DOI: 10.4064/bc104-0-3


The problem of completeness of the forward rate based bond market model driven by a Lévy process under the physical measure is examined. The incompleteness of market in the case when the Lévy measure has a density function is shown. The required elements of the theory of stochastic integration over the compensated jump measure under a martingale measure are presented and the corresponding integral representation of local martingales is proven.


  • Michał BarskiFaculty of Mathematics and Computer Science
    University of Leipzig
    Augustusplatz 10
    04109 Leipzig, Germany
    Faculty of Mathematics
    Cardinal Stefan Wyszyński University in Warsaw
    Wóycickiego 1/3
    01-938 Warsaw, Poland

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