The aim of this paper was to make stochastic framework of well-known chain ladder algorithm through these two models: Chain ladder model without distributional assumption; Overdispersed Poisson model. Chain ladder algorithm is deterministic process that does not provide any information about the reliability of the results. Because of that, it is necessary to describe it more detailed in terms of mathematical theory to achieve quantification of uncertainty. First model is natural extension of algorithm because it follows its logic through stochastic modelling. It is gradually built up to time series model which will help us measure variability with all assumptions needed for that, such as independence of accident year. Second model is based on assumption that all incremental claims have overdispersed Poisson distribution which is completely different view than the Chain ladder model. In the background of this approach is the theory of generalized linear models with a restriction on the Poisson distribution from the exponential family. These models were chosen for stochastic framework because they produce identical expected claim reserve with different variability, more precisely with different second and higher moments. This is consequence of the assumptions they are built on. Also, both are suitable for extension with bootstrap method which provides us additional valuable information - the distribution of claim reserves. To make all the results comparable, we used mean square error of prediction as a measure of variability . In the second part of paper specific data set was chosen on which all 4 models were applied: Chain ladder model without distributional assumption, Overdispersed Poisson model, Bootstrap method based on chain ladder model, Bootstrap method based on overdispersed Poisson model. The models were broke down through few stages beginning with graphical analysis of the residuals through testing specific assumptions to the last part which is presentation and comparison of the results.