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Towards a general theory of bond markets
Authors:Tomas Björk  Giovanni Di Masi  Yuri Kabanov  Wolfgang Runggaldier
Affiliation:Department of Finance, Stockholm School of Economics, Box 6501, S-113 83 Stockholm, Sweden, SE
Dipartimento di Matematica Pura et Applicata, Universitá di Padova, Via Belzoni 7, I-35131 Padova, Italy, IT
Central Economics and Mathematics Institute of the Russian Academy of Sciences and Laboratoire de Mathématiques, Université de Franche-Comté, 16 Route de Gray, F-25030 Besan?on Cedex, France, FR
Dipartimento di Matematica Pura et Applicata, Universitá di Padova, Via Belzoni 7, I-35131 Padova, Italy, IT
Abstract:The main purpose of the paper is to provide a mathematical background for the theory of bond markets similar to that available for stock markets. We suggest two constructions of stochastic integrals with respect to processes taking values in a space of continuous functions. Such integrals are used to define the evolution of the value of a portfolio of bonds corresponding to a trading strategy which is a measure-valued predictable process. The existence of an equivalent martingale measure is discussed and HJM-type conditions are derived for a jump-diffusion model. The question of market completeness is considered as a problem of the range of a certain integral operator. We introduce a concept of approximate market completeness and show that a market is approximately complete iff an equivalent martingale measure is unique.
Keywords::Bond market   term structure of interest rates   stochastic integral   Banach space-valued integrators   measure-valued portfolio   jump-diffusion model   martingale measure   arbitrage   market completeness. ?JEL classification:G10   E43 ?Mathematics Subject Classification (1991):60H05   90A09
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