Nonparametric evaluation of continuous r-year deferred m-year term life annuity using information on probabilistic characteristics of lifetime - Dmitriev, Yury G. (Вестник Томского государственного университета. Управление, вычислительная техника и информатика)
The theory of pension annuities is closely related to the ideology of net premiums of the life insurance theory. The mathematical theory of insurance is widely used to solve many problems that are determined by the requirements of the market economy. The requirements of practice stimulate the development of insurance theory and the closely related theory of annuities and force researchers to turn to more complex mathematical models in this area. New methods of calculating annuities appear that reduce the time for making optimal decisions in the absence of sufficient information about the markets of new types of pension services. The article considers the problem of estimating continuous r-year deferred m-year term life annuity with making use of information on probabilistic characteristics of lifetime. Insurance companies often offer their clients to conclude contracts of r-year deferred m-year annuities. Nonparametric estimators of life annuities are constructed from data on the lifetimes of individuals. Found the principal terms of the asymptotic mean squared errors (MSEs) of the proposed estimators; their asymptotic normality is proved. It is shown that the use of auxiliary information often leads to a lower MSE of the modified estimator compared to the MSE of the traditional estimator. An adaptive estimator is proposed that can be applied in practice.