## Using parametric bootstrap to introduce and manage uncertainty: replicated loaded insurance life tables.(English)Zbl 1426.91231

Summary: Insurance companies develop loaded life tables to protect themselves against deviations, for example, in the number of expected deaths or in the (residual) expectation of life of their insured. In doing so, however, the single random vector of experience crude death rates from which loaded tables are constructed is treated as deterministic or, at best, as a single realization of an underlying stochastic process, omitting the fact that it is estimated and subject to error and uncertainty. This can result in serious consequences for the insurer. To solve this problem, we follow the example of other researchers and propose a method to replicate loaded life tables using parametric bootstrap. We focus on estimating period-loaded life tables from company portfolios, where the sizes of the exposed-to-risk populations are significantly smaller than those of general populations. If we have a set of $$B$$ loaded life tables, the average behavior and some extreme values can be computed and subsequently used in managing premiums or reserves. This article offers life insurers a simple way of incorporating the experience uncertainty in actuarial tasks (for example, in pricing) by comparing the limits of the confidence intervals obtained between parametric bootstrap and classical approaches (such as limit theorems).

### MSC:

 91G05 Actuarial mathematics 62P05 Applications of statistics to actuarial sciences and financial mathematics 62F40 Bootstrap, jackknife and other resampling methods

### Software:

R; Human Mortality; GoFKernel; nls2; bootstrap
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