Infinite dimensional affine term structure models under incomplete information

Abstract: The first part of the dissertation extends some important results in the classical theory of finite dimensional affine processes to infinite dimensional separable Hilbert spaces. In particular, a necessary and sufficient condition for a continuous Markov diffusion process to be affine is given. Based on the extended theory, two affine term structure models are introduced and the existence and uniqueness of the two models are studied. The second part concentrates on a non-linear filtering problem with infinite dimensional observations and the Kushner-Stratonovich equation under the infinite dimensional observation setting is derived. Finally, the obtained results are applied to study the Kalman-Bucy filter with infinite dimensional observations. It is proved that the filter has a Gaussian distribution and the evolution equations of the mean and the covariance of the filter are deduced from the Kushner-Stratonovich equation