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Towards a general theory of bond markets (*)

  • Giovanni Di Masi

    (Dipartimento di Matematica Pura et Applicata, Universitá di Padova, Via Belzoni 7, I-35131 Padova, Italy)

  • Tomas Björk

    (Department of Finance, Stockholm School of Economics, Box 6501, S-113 83 Stockholm, Sweden)

  • Wolfgang Runggaldier

    (Dipartimento di Matematica Pura et Applicata, Universitá di Padova, Via Belzoni 7, I-35131 Padova, Italy)

  • Yuri Kabanov

    (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 Besançon Cedex, France)

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.

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Article provided by Springer in its journal Finance and Stochastics.

Volume (Year): 1 (1997)
Issue (Month): 2 ()
Pages: 141-174

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Handle: RePEc:spr:finsto:v:1:y:1997:i:2:p:141-174
Note: received: March 1996; final version received: October 1996 To the memory of our friend and colleague Oliviero Lessi.
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