Parametric and Nonparametric Bootstrap in Actuarial Practice

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 distributions, e.g., Gompertz’s model of force of mortality, or parametric models of the yield curve process. Modern actuarial science has introduced probabilistic models for all input variables in studying insurance firm, and in the whole company models. These new methodologies are based on the theoretical work in mathematical finance which shows that the market, or fair value of insurance liabilities, and indeed, the market value of the insurance firm, can be determined using the general approach developed for contingent claims valuation. While this is theoretically appealing and justified, the central dilemma in modeling insurance company, i.e., its assets and liabilities, is the choice of an appropriate probability distributions, or stochastic processes, governing the evolution of the underlying variables such as interest rates, or asset returns in general, withdrawals or lapses, and mortality. The traditional approaches to this problem have been based on the parametric models. The last two decades have brought about a rich body of new research in nonparametric statistics. This work is intended at showing direct application of a specific nonparametric methodology in actuarial models. The methodology researched here is that of the bootstrap, and more generally, resampling. We develop the bootstrap model alternative on both the asset and liability side. First, we show how bootstrap can be used successfully in enhancing a parametric mortality law suggested by Carriere (1992). Next, we develop a whole company asset-liability model to study a bootstrap alternative to lognormal and stable Paretian models of interest rate process. The 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 for the existing models.