Nonparametric estimation of actuarial values

Abstract

Recently, the so-called δ-method has been given renewed attention in survival analysis, mostly due to an article by Gill ( 1989). In this paper we apply the δ-method to functionals that arise when one uses nonparametric estimators to estimate actuarial values from life history data. We obtain general formulas for the asympotic distribution of nonparametric actuarial value estimators. To illustrate these calculations, we compare the large sample properties of traditional and nonparametric estimators of actuarial values. This is done for two insurance contracts, a term insurance contract and a disability annuity, under the model assumptions specified in the Danish technical basis G-82.

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