Applications of resampling methods in actuarial practice

Actuarial analysis can be viewed as the process of studying profitability and solvency of an insurance firm under a realistic and integrated model of key input random variables such as loss frequency and severity, expenses, reinsurance, interest and inflation rates, and asset defaults. Traditional models of input variables have generally fitted parameters for a predetermined family of probability distributions. In this paper we discuss applications of some modern methods of non-parametric statistics to modeling loss distributions, and possibilities of using them for modeling other input variables for the purpose of arriving at an integrated company model. Several examples of inference about the severity of loss, loss distributions percentiles and other related quantities based on data smoothing, bootstrap estimates of standard error and bootstrap confidence intervals are presented. The examples are based on reallife auto injury claim data and the accuracy of our methods is compared with that of standard techniques. Model adjustment for inflation and bootstrap techniques based on the Kaplan–Meier estimator, useful in the presence of policies limits (censored losses), are also considered.