Title: Computational tools for IBNR reserves calculation Author: Bc. Štěpán Gregor Department: Department of Probability and Mathematical Statistics Supervisor: Mgr. Helga Krafferová, UNIQA pojišťovna, a.s. Supervisor' s e-mail address: Helga.Krafferova@uniqa.cz Abstract: Technical provisions represent the liability of the insurance company to its clients. In this work we focus on the computational tools of incurred but not reported claims. The most popular calculation method is probably the chain-ladder method which will be in detail analyzed in this thesis. Finally, by applying the theory in this work we will demonstrate the calculation in the own developed software. Keywords: Insurance, IBNR reserve, chain-ladder

Title: Munich chain ladder method Author: Bc. Veronika Janáková Department: Department of probability and mathematical statistic Supervisor: Mgr. Martin Pleška Supervisor's e-mail address: martin.pleska@cz.pwc.com Abstract: The insurance company is obliged to create technical reserves to cover the risk from insurance activities. One of the main reserves in non-life insurance is the IBNR reserve - the reserve to cover the damages that already exist, but that have not been reported to the insurance company yet. The content and the general aim of this thesis is to provide a better orientation in the method used in the estimation of the reserve IBNR - the Munich Chain Ladder Method. Munich Chain Ladder Method was created as a modification of the standard Chain Ladder calculation - one of the most used methods in the estimation of the IBNR reserve. The thesis focuses on the reasons that led to the modification of standard Chain Ladder calculation and explains the calculation of the modified method. It presents the application ot the method on the real data as well as the comparison with the results of the classical and less complicated Chain Ladder method. Keywords: IBNR reserve, chain ladder, Munich chain ladder 1

This text describes wide variety of models for IBNR reserve estimation, among them we can find chain ladder, Munich chain ladder, Cape Cod or regression methods. Especially, it aims at identification of model assumptions, its verification, impacts of their non-fulfillment and resulting model modification. Moreover, this work deals with anomalies and specificity of historical data and tries to suggest solutions for this problems. The last part of the thesis is dedicated to real analysis of motor third party liability.

The main goal of this Diploma thesis is to describe an approach for modeling run-off triangles of nonlife insurance (calculation of IBNR reserve) based on state space models and apply the method to the selected run-off triangles. In difference from (Atherino a kol., 2010) the KFAS package in R software is used for modeling purposes in the numerical study at the end of the thesis. One provides a preview of various possibilities of data and model adjustment applied to the same run-off triangles in order to asses added value of these steps (logartihmic transformation of input data, interventions for outliers etc.). A special attention is devoted to lognormal modification of the basic state space model. An integral part of the numerical study in the thesis is a residual diagnostic of models and simulation approach to IBNR reserves. 1