Abstract.
We propose here a theory of cylindrical stochastic integration, recently developed by Mikulevicius and Rozovskii, as mathematical background to the theory of bond markets. In this theory, since there is a continuum of securities, it seems natural to define a portfolio as a measure on maturities. However, it turns out that this set of strategies is not complete, and the theory of cylindrical integration allows one to overcome this difficulty. Our approach generalizes the measure-valued strategies: this explains some known results, such as approximate completeness, but at the same time it also shows that either the optimal strategy is based on a finite number of bonds or it is not necessarily a measure-valued process.
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Received: November 2002,
Mathematics Subject Classification:
60H05, 60G60, 90A09
JEL Classification:
G10, E43
The first author gratefully acknowledges financial support from the CNR Strategic Project “Modellizzazione matematica di fenomeni economici”. We thank professors A. Bagchi, R. Douady and J. Zabczyk for helpful discussions. A special thanks goes to professors T. Björk, Y. Kabanov and W. Schachermayer for comments and suggestions which contributed to improve the final version of this paper.
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Donno, M.D., Pratelli, M. On the use of measure-valued strategies in bond markets. Finance and Stochastics 8, 87–109 (2004). https://doi.org/10.1007/s00780-003-0102-7
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DOI: https://doi.org/10.1007/s00780-003-0102-7