Journal of Applied Mathematics and Stochastic Analysis
Volume 2006 (2006), Article ID 53104, 26 pages
doi:10.1155/JAMSA/2006/53104
Abstract
We study the linear filtering problem for systems driven by
continuous Gaussian processes V(1) and V(2) with memory
described by two parameters. The processes V(j) have the virtue that they possess stationary increments and simple
semimartingale representations simultaneously. They allow for
straightforward parameter estimations. After giving the
semimartingale representations of V(j) by innovation theory,
we derive Kalman-Bucy-type filtering equations for the systems. We
apply the result to the optimal portfolio problem for an investor
with partial observations. We illustrate the tractability of the
filtering algorithm by numerical implementations.