Completeness of bond market driven by L\'evy process

Abstract

The completeness problem of the bond market model with the random factors determined by a Wiener process and Poisson random measure is studied. Hedging portfolios use bonds with maturities in a countable, dense subset of a finite time interval. It is shown that under natural assumptions the market is not complete unless the support of the L\'evy measure consists of a finite number of points. Explicit constructions of contingent claims which can not be replicated are provided.