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In this paper, we establish a robustification of an on-line algorithm formodelling asset prices within a hidden Markov model (HMM). In this HMMframework, parameters of the model are guided by a Markov chain in discretetime, parameters of the asset returns are therefore able to switch betweendifferent regimes. The parameters are estimated through an on-line algorithm,which utilizes incoming information from the market and leads to adaptiveoptimal estimates. We robustify this algorithm step by step against additiveoutliers appearing in the observed asset prices with the rationale to betterhandle possible peaks or missings in asset returns.

Robustification of Elliott's on-line EM algorithm for HMMs