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

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 is presented and the corresponding integral representation of local martingales is proven.