Bootstrap Methods for Claims Reserving: R Language Approach

Abstract

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.