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The Term Structure of Interest Rates as a Random Field: a Stochastic Integration Approach

In: Stochastic Processes And Applications To Mathematical Finance

Author

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  • Marzia De Donno

    (Dipartimento di Matematica, Università di Pisa, via Buonarroti 2, 56127 Pisa, Italy)

Abstract

We investigate the term structure of zero coupon bonds, in the case where the forward rate evolves as a Wiener sheet. We introduce a definition of stochastic integral with respect to a continuous semimartingale with values in the set of continuous functions and characterize the dynamics of the zero coupon bonds. We also define a notion of generalized strategy, in order to admit the (theoretical) possibility of investing in a continuum of bonds. Finally we study the problem of utility maximization from terminal wealth in this setting and deduce a "mutual fund" theorem.

Suggested Citation

  • Marzia De Donno, 2004. "The Term Structure of Interest Rates as a Random Field: a Stochastic Integration Approach," World Scientific Book Chapters, in: Jiro Akahori & Shigeyoshi Ogawa & Shinzo Watanabe (ed.), Stochastic Processes And Applications To Mathematical Finance, chapter 2, pages 27-52, World Scientific Publishing Co. Pte. Ltd..
    • Handle: RePEc:wsi:wschap:9789812702852_0002
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    Cited by:

    1. M. De Donno & M. Pratelli, 2006. "A theory of stochastic integration for bond markets," Papers math/0602532, arXiv.org.
    2. Jirô Akahori & Takahiro Tsuchiya, 2006. "What is the Natural Scale for a Lévy Process in Modelling Term Structure of Interest Rates?," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 13(4), pages 299-313, December.

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