The term structure of interest rates as a random field: a stochastic integration approach

Marzia De Donno

doi:10.1142/9789812702852_0002

The term structure of interest rates as a random field: a stochastic integration approach

Marzia De Donno

Risultato della ricerca: Contributo in libro › Contributo a conferenza

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

Lingua originale	Inglese
Titolo della pubblicazione ospite	Ritsumeikan International Symposium on Stoch. Proc. and Appl. to Math. Fin
Pagine	27-52
Numero di pagine	26
DOI	https://doi.org/10.1142/9789812702852_0002
Stato di pubblicazione	Pubblicato - 2004
Evento	International Symposium Stochastic Processes and Application to Mathematical Finance - Ritsumeikan University (Japan) Durata: 5 mar 2003 → 9 mar 2003

Convegno

Convegno	International Symposium Stochastic Processes and Application to Mathematical Finance
Città	Ritsumeikan University (Japan)
Periodo	5/3/03 → 9/3/03

Keywords

Infinite-dimensional stochastic integration, Wiener sheet, bond market, term structure of interest rates, generalized strategy, utility maximization.

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10.1142/9789812702852_0002

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title = "The term structure of interest rates as a random field: a stochastic integration approach",

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",

keywords = "Infinite-dimensional stochastic integration, Wiener sheet, bond market, term structure of interest rates, generalized strategy, utility maximization., Infinite-dimensional stochastic integration, Wiener sheet, bond market, term structure of interest rates, generalized strategy, utility maximization.",

author = "\{De Donno\}, Marzia",

year = "2004",

doi = "10.1142/9789812702852\_0002",

language = "English",

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PY - 2004

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N2 - 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

AB - 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

KW - Infinite-dimensional stochastic integration, Wiener sheet, bond market, term structure of interest rates, generalized strategy, utility maximization.

UR - http://hdl.handle.net/10807/168921

U2 - 10.1142/9789812702852_0002

DO - 10.1142/9789812702852_0002

M3 - Conference contribution

SN - 9812387781

SP - 27

EP - 52

BT - Ritsumeikan International Symposium on Stoch. Proc. and Appl. to Math. Fin

T2 - International Symposium Stochastic Processes and Application to Mathematical Finance

Y2 - 5 March 2003 through 9 March 2003

ER -

The term structure of interest rates as a random field: a stochastic integration approach

Abstract

Convegno

Keywords

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