Bootstrap methods have been used by actuaries for a long time to predict future claims cash flows and their variability. This work aims to illustrate the use of bootstrap methods in practice, taking as an example the claims development data of the personal accident portfolio from the largest insurance company in Albania, over a period of 10 years. It is not the objective of this work to provide a theoretical analysis of the bootstrap methods, rather, this work focuses on highlighting the benefits of using bootstrap methods to predict the distribution of future claims development, and estimate the standard error, for a better risk assessment of liabilities within insurance companies. This work is divided into two well-differentiated phases: the first is to select the theoretical probability distribution that best fits the available claims dataset. Comparison of distributions is facilitated by the possibilities offered by the R programming languages. Both, the maximum likelihood parameter estimation method and the chi-square goddess goodness of fit test, are used to specify the probability distribution that best fits the data, among a family of predefined distributions. The results show that the Gamma distribution better describes the claim development data. The next phase is to use bootstrap methods, based on the selected distribution, to estimate the ultimate value of claims, the claims reserve, and their standard error.

Stochastic methods of reserves estimation serve to assess the technical provisions of outstanding claims and forecast cash payments of claims in the coming years. The chain ladder model developed by Mack is the more prevalent model. The main deficiency in the chain-ladder model is that the chain-ladder model depends on the last observation on the diagonal. If this last observation is an outlier, this outlier will be projected to the ultimate claim. One of the possibilities to smooth outliers on the last observed diagonal is to robustify such observations, making use of the maximum likelihood estimation along with the common Loss Development Factor (LDF) curve fitting and Cape Cod (CC) techniques. This paper aims to highlight the advantages of using these methods for the best estimate of claims reserves in the Domestic Motor Third Party Liability portfolio. The maximum–likelihood parameter estimation and Chi-square test, are used to specify the probability distribution that best fits the data. Using the Standard Chain Ladder method, LDF, and CC method the claims reserve is calculated based on the run-off triangles of paid claims or the run-off triangles of the incurred claims. Many times, the projections based on the paid claims are different than the projections based on the incurred claims. The solution for this problem is the Munich Chain Ladder method.