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Estimation of the present values of net premiums and life annuities for the different actuarial models Y. G. Dmitriev, O. V. Gubina, G. M. Koshkin

By: Dmitriev, Yury GContributor(s): Gubina, Oxana V | Koshkin, Gennady MMaterial type: ArticleArticleContent type: Текст Media type: электронный Subject(s): непараметрическая оценка | аннуитет | асимптотическая нормальность | среднеквадратичная ошибкаGenre/Form: статьи в сборниках Online resources: Click here to access online In: Applied methods of statistical analysis. Statistical computation and simulation : proceedings of the international workshop, 18-20 September 2019 P. 30-46Abstract: The paper deals with the estimation problem of the actuarial present values of the continuous individual net premiums and connected with these characteristics life annuities. We considered the following actuarial models: the whole life insurance, n-year term life insurance, q-year deferred life insurance, and n-year endowment life insurance. We synthesize nonparametric estimators of net premiums and life annuities for these statuses. The main parts of the asymptotic mean square errors of the estimators and their limit distributions are found. The simulations show that the empirical mean square errors of estimators decrease when the sample size increases. Also, when the model distribution is changed, the nonparametric estimators are more adaptable in comparison with parametric estimators, oriented on the best results only for the given distributions.
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The paper deals with the estimation problem of the actuarial present values
of the continuous individual net premiums and connected with these characteristics
life annuities. We considered the following actuarial models: the whole life
insurance, n-year term life insurance, q-year deferred life insurance, and n-year
endowment life insurance. We synthesize nonparametric estimators of net premiums
and life annuities for these statuses. The main parts of the asymptotic
mean square errors of the estimators and their limit distributions are found.
The simulations show that the empirical mean square errors of estimators decrease
when the sample size increases. Also, when the model distribution is
changed, the nonparametric estimators are more adaptable in comparison with
parametric estimators, oriented on the best results only for the given distributions.

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