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
De Donno, M., The term structure of interest rates as a random field: a stochastic integration approach, Paper, in Ritsumeikan International Symposium on Stoch. Proc. and Appl. to Math. Fin, (Ritsumeikan University (Japan), 05-09 March 2003), Editors: J. Akahori, S. Ogawa, S. Watanabe. Publi, Ritsumeikan 2004: 27-52. 10.1142/9789812702852_0002 [http://hdl.handle.net/10807/168921]
The term structure of interest rates as a random field: a stochastic integration approach
De Donno, Marzia
2004
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
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