ABSTRACT
The filtering problem is about predicting non observable random vectors Z1, Z2, . . ., called the signal, by using observations Y1, . . . , Yn linked in a certain way to the signal. In fact, what we really want to do is to find the conditional distribution of Zi+k given Y1, . . . , Yi, for k ≥ 0. We also want to rapidly incorporate new observations Yi+1, Yi+2, . . .. Here are some examples of signals in financial applications: stochastic volatility, detention yield, betas of dynamic portfolios, regimes. Observations could be, for example, the returns of an asset, values of futures contracts, etc.
