  In this paper, we establish a robustification of an on-line algorithm for
modelling asset prices within a hidden Markov model (HMM). In this HMM
framework, parameters of the model are guided by a Markov chain in discrete
time, parameters of the asset returns are therefore able to switch between
different regimes. The parameters are estimated through an on-line algorithm,
which utilizes incoming information from the market and leads to adaptive
optimal estimates. We robustify this algorithm step by step against additive
outliers appearing in the observed asset prices with the rationale to better
handle possible peaks or missings in asset returns.
