  Three situations in which filtering theory is used in mathematical finance
are illustrated at different levels of detail. The three problems originate
from the following different works: 1) On estimating the stochastic volatility
model from observed bilateral exchange rate news, by R. Mahieu, and P.
Schotman; 2) A state space approach to estimate multi-factors CIR models of the
term structure of interest rates, by A.L.J. Geyer, and S. Pichler; 3)
Risk-minimizing hedging strategies under partial observation in pricing
financial derivatives, by P. Fischer, E. Platen, and W. J. Runggaldier; In the
first problem we propose to use a recent nonlinear filtering technique based on
geometry to estimate the volatility time series from observed bilateral
exchange rates. The model used here is the stochastic volatility model. The
filters that we propose are known as projection filters, and a brief derivation
of such filters is given. The second problem is introduced in detail, and a
possible use of different filtering techniques is hinted at. In fact the
filters used for this problem in 2) and part of the literature can be
interpreted as projection filters and we will make some remarks on how more
general and possibly more suitable projection filters can be constructed. The
third problem is only presented shortly.
