Towards a general theory of bond markets (*)

Giovanni Di Masi, Tomas Bjork, Wolfgang Runggaldier and Yuri Kabanov
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Giovanni Di Masi: Dipartimento di Matematica Pura et Applicata, Universitá di Padova, Via Belzoni 7, I-35131 Padova, Italy
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
Authors registered in the RePEc Author Service: Юрий Михайлович Кабанов

Finance and Stochastics, 1997, vol. 1, issue 2, 174 pages

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. (search for similar items in EconPapers)
JEL-codes: E43 G10 (search for similar items in EconPapers)
Date: 1997
Note: received: March 1996; final version received: October 1996 To the memory of our friend and colleague Oliviero Lessi.
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Citations: View citations in EconPapers (14)

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Working Paper: Towards a General Theory of Bond Markets (1996)
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