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.

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.
2004
9812387781
Ritsumeikan International Symposium on Stoch. Proc. and Appl. to Math. Fin.
DE DONNO, Marzia
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11565/192755
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