White Noise Approach to Interest Rate Models

We discuss the class of models for the term structure of forward interest rates when the dynamics involve the following stochastic evolution equation: dX(t) = [ AX(t) + F (t) ] dt+BdW (t), X(0) = X0, where X takes values in a separable Hilbert space H. Here A is the generator of a semigroup, B : H → H is a bounded linear operator, W (·) is an H-valued cylindrical Wiener process. This model includes in particular the HJM model (in the parametrization of Musiela), second order term structure models and generalizations. Mathematics Subject Classification 2000: 91B28, 60H40, 60H30, 60G20, 47D06, 60J70