This work makes use of three methodologies for modeling IBNR data arranged in the runoff triangle with a tail effect, and evaluates their performances in four empirical examples. The first methodology is the traditional chain ladder, duly extended to calculate a reserve corresponding to the calendar year. The second methodology remains on linear regression models with heteroscedastic errors, under the well-established double index notation of the triangle. The third methodology uses the linear state space modeling and the theory of the Kalman filter, adopting, this time, the row-wise ordering proposed by Atherino et al. (2010). For each approach, theoretical results and numerical implementations are obtained, where both the punctual IBNR reserve estimators and their corresponding theoretical mean square errors are considered. The main conclusions from this Dissertation are: (i) even thought proving to be superior to the chain ladder, none of the remaining two approaches seems to outperform the other; (ii) the adding of a tail effect does not entail major theoretical and/or computational problems; and (iii) the approaches have uncovered stylized facts that would enable the planning of softwares for IBNR reserve estimation.