Emerging Applications of the Resampling Methods in Actuarial Models

Uncertainty of insurance liabilities has always been the key issue in actuarial theory and practice. This is represented for instance by study and modeling of mortality in life insurance and loss distributions in traditional actuarial science. These models have evolved from early simple deterministic calculations to more sophisticated, probabilistic ones. Such probabilistic models have been traditionally built around parameters characterizing certain probability laws, e.g., Gompertz’s model of force of mortality, or parametric models of the yield curve process. In this article we describe the methodology of the bootstrap, and more generally, resampling and show some of its possible advantages in describing the underlying probability distributions. We provide two detailed examples of application of the resampling methods. First, we show how bootstrap can be used successfully to enhance a parametric mortality law suggested by Carriere (1992). Next, we develop a whole company asset-liability model to study the nonparametric bootstrap alternative to lognormal and stable Paretian models of interest rate process proposed by Klein (1993). Our results indicate that bootstrap can be instrumental in understanding the rich structure of random variables on the asset and liability sides of an insurance firm balance sheet, and in error estimation in both parametric and non-parametric setting.