Bond market structure in the presence of marked point processes

We investigate the term structure of zero coupon bonds when interest rates are driven by a general marked point process as well as by a Wiener process. Developing a theory that allows for measure-valued trading portfolios, we study existence and uniqueness of a martingale measure. We also study completeness and its relation to the uniqueness of a martingale measure. For the case of a finite jump spectrum we give a fairly general completeness result and for a Wiener-Poisson model we prove the existence of a time-independent set of basic bonds. We also give sufficient conditions for the existence of an affine term structure.