In this presentation, based on Barbu et al., 2017, we are interested in applications of statistical techniques for Markov chains in nancial mathematics. We have modelled through a Markov chain the time evolution of the dividend growth factor of a stock. We were interested in estimating the rst two moments of the price of the stock and also in forecasting the price of the stock within n time units. This work represents further advancements of the Markov chain stock model proposed in Ghezzi and Piccardi, 2003. We give theoretical results about the consistency and asymptotic normality of the estimated quantities and apply our ndings to real dividend data. The statistical techniques for Markov chains are mainly based on Sadek and Limnios, 2002. These results were integrated into a semi-Markov framework as provided by D'Amico, 2013, where the semi-Markov hypothesis was advanced and validated on real data. A further generalization was given in D'Amico, 2016, where a continuous state space semi-Markov model is considered for the computation of the fundamental price and risk of the stock. Acknowledgement. The research work of Vlad Stefan Barbu was partially supported by the projects XTerM { Complex Systems, Territorial Intelligence and Mobility (2014{2018) and MOUSTIC { Random Models and Statistical, Informatics and Combinatorics Tools (2016{2019). The research work of Guglielmo D'Amico was partially supported by the Federation NormandyMathematics, France, by o ering the opportunity of spending several periods as visiting professor in the Laboratory of Mathematics Raphael Salem, Department of Mathematics, University of Rouen and in Laboratory of Mathematics Nicolas Oresme, Department of Mathematics, University of Caen, France.