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
|Convegno||International Symposium Stochastic Processes and Application to Mathematical Finance|
|Città||Ritsumeikan University (Japan)|
|Periodo||5/3/03 → 9/3/03|
- Infinite-dimensional stochastic integration, Wiener sheet, bond market, term structure of interest rates, generalized strategy, utility maximization.