(), Giovanni di Masi
, Yuri Kabanov
and Wolfgang Runggaldier
Tomas Björk: Department of Finance, Postal: Stockholm School of Economics, Box 6501, 113 83 Stockholm, Sweden
Giovanni di Masi: Dipartimento di Matematica Pura et Applicata, Postal: Universitá di Padova, Via belzoni 7, 351 31 Padova, Italy
Yuri Kabanov: Laboratoire de Mathématiques, Postal: Université de Franche-Comté, 16 Route de Gray, F-25030 Besançon Cedex France
Wolfgang Runggaldier: Dipartimento di Matematica Pura et Applicata, Postal: Universitá di Padova, Via Belzoni 7, 351 31 Padova, Italy
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 if 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
33 pages, December 1996
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