On the use of measure-valued strategies in bond markets

Marzia De Donno and Maurizio Pratelli ()

Finance and Stochastics, 2004, vol. 8, issue 1, 87-109

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. Copyright Springer-Verlag Berlin/Heidelberg 2004

Keywords: Bond markets; term structure of interest rates; measure-valued portfolio; cylindrical stochastic integration; covariance spaces; market completeness (search for similar items in EconPapers)
Date: 2004
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DOI: 10.1007/s00780-003-0102-7

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