Kolektivní model rizika v neživotním pojištění

This work aims to model the ultimate claims amount and 95% quantile for simulated homogeneous portfolio of insurance company. For this paper, the creation of a tool for an artificial database imitating real view on creation and process of damages liquidated by insurance companies. Simulated information about damages are created via a special programming language SQL. Negative-binominal distribution is used for simulating a number of claims and log-normal distribution for claims amount. These two distributions are base for using collective risk model. Other indicators in the database are reporting time delays, gradual payment time delays to the possible closing time, and reserve errors (RBNS). Once the database has been created, the work will deal with development triangles (incremental and cumulative) number and amount of paid claims via MS Excel. After that, the analysis of the ultimate claim amount will be created owing to four methods (formulas; development triangle; simulation; Panjer formula). Through utilising the last two methods, the different programming language called R will be necessary to facilitate this. The intended result of this work is creation of pseudorandom database and to evaluate used methods for the collective risk model in terms of their mathematical properties and ilustration on the numerical example. It was found out, that by comparing used methods of estimates for the ultimate claim amount, the simulation method was the most accurate. For comparing estimates for standard deviation method using development triangles was the most accurate.