Completeness of bond market driven by Lévy process

The completeness problem of the bond market model with noise given by the independent Wiener process and Poisson random measure is studied. Hedging portfolios are assumed to have maturities in a countable, dense subset of a finite time interval. It is shown that under some assumptions the market is not complete unless the support of the Levy measure consists of a finite number of points. Explicit constructions of contingent claims which can not be replicated are provided.