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Bond market structure in the presence of marked point processes. (English) Zbl 0884.90014

Summary: 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.

MSC:

91B28 Finance etc. (MSC2000)
60G35 Signal detection and filtering (aspects of stochastic processes)
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