Estimation of the Present Values of Life Annuities for the Different Actuarial Models

Кошкин, Г. М.; Gubina, Oxana V.

doi:10.1109/smrlo.2016.89

Cited by 3 publications

(4 citation statements)

References 11 publications

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“…Following (Koshkin, Gubina, 2016;Dmitriev, Kohkin, 2018;Castellares, Patricio and Lemonte, 2022), the continuous whole life insurance at age x is given by 1…”

Section: Discussionmentioning

confidence: 99%

Mathematical Derivations of Actuarial Present Value for the Fully Continuous Whole Life Assurances from the Theoretical Market Price

Ogungbenle,

Ezekiel

2023

J. Multidisc. Res. Adv.

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Many current mortality tables are computationally Makehamised but technically devoid of continuous key life table functions such as and because of the underlying sophisticated mortality functions and the complex methods of computation which usually do not incorporate the market price. The computationally advanced Moore’s model, which does not endorse the market pricing mechanisms offers one of the most complex analytical results that seems not user friendly in actuarial literature. As a result of the Moore’s complexity, we offer the Gradshteyn and Ryzhik’s analytic integral as an alternative solution to examine the contingency issues involving the estimation of actuarial present values of the continuous whole life annuities. In this study, the objective are to (i) estimate the parameters of GM (1,2) through the method of equidistant points according to the natural order of human age (ii) Apply the mean value theorem to construct the survival probability function under the framework of policy modifications (iii) Develop a closed form pricing formula for the continuous whole life annuity and continuous whole life insurance. The Gradshteyn and Ryzhik’s analytic integral has eliminated the Moore’s complexities associated with symbolic computations such that the continuity assumption applied allows us to compute the continuous life annuity with expedience. Computational evidence further shows that the continuous life annuity reduces with age confirming that life annuities is a decreasing function.

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“…Following (Koshkin, Gubina, 2016;Dmitriev, Kohkin, 2018;Castellares, Patricio and Lemonte, 2022), the continuous whole life insurance at age x is given by 1…”

Section: Discussionmentioning

confidence: 99%

Mathematical Derivations of Actuarial Present Value for the Fully Continuous Whole Life Assurances from the Theoretical Market Price

Ogungbenle,

Ezekiel

2023

J. Multidisc. Res. Adv.

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“…Assuming the policyholder is still alive until age of + , then the payment would take a place at = 0, 1, 2, … , − 1. If we denote that the present value of this annuity by , then we obtain (Koshkin & Gubina, 2016…”

Section: B Literature Reviewmentioning

confidence: 99%

Mortality Projection on Indonesia's Abridged Life Table to Determine the EPV of Term Annuity

Siswono¹,

Azmi²,

Syaifudin³

2021

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The life insurance industries usually use the Life Table for the valuation process, especially in calculating premiums and policy values of a policy. However, the Life Table is rarely updated; and it may even take years before they are updated. This happens because the insurers believe that the information in the Life Table is still related to the current state of a country and for the next several years. In fact, data and information related to mortality rates in a country are constantly changing and always being updated annually. Therefore, as an approach, researchers use the projection of mortality to approach the mortality rate in the future. Thus, future mortality data can be predicted so that better policies can be made by the governments or insurance industries. In this study, the Abridged Life Table of Indonesia is used in the projection of mortality for both sexes (male and female) of the population in Indonesia. The results of mortality projection are then used to calculate the Expected Present Value (EPV) of a term annuity-due under uniform distribution of deaths (UDD) for several values of and ages. The results obtained show that there is a decrease in the value of the mortality rate in the next few years. Therefore, it can be assumed that there is a possibility for longevity risk to occur in the future.

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“…x be an individual's age on the moment of payments start, X be his lifetime, Then, by averaging the random variable z(x) (1), we get the formula of the whole life annuity (see [2][3][4]):…”

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confidence: 99%

“…XX of N individuals' lifetimes. Now, separately estimate the numerator and denominator in (2). The substitution of unknown function S(x) for its nonparametric estimator Estimation of present value of whole life annuity using information about expectation of life…”

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confidence: 99%

Estimation of present value of whole life annuity using information about expectation of life

Dmitriev¹,

Кошкин²

2018

Tomsk State University Journal of Control and Computer Science

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The paper deals with the estimation problem of the actuarial present value of the continuous whole life annuity using auxiliary information about the expectation of life. Nonparametric estimators of life annuity are constructed by individuals' death moments. It is shown that the usage of such auxiliary information can often provide the mean squared error (MSE) smaller than that of standard estimators. An adaptive estimator is also proposed. The asymptotic normality of all these estimators is proved.

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Estimation of the Present Values of Life Annuities for the Different Actuarial Models

Cited by 3 publications

References 11 publications

Mathematical Derivations of Actuarial Present Value for the Fully Continuous Whole Life Assurances from the Theoretical Market Price

Mathematical Derivations of Actuarial Present Value for the Fully Continuous Whole Life Assurances from the Theoretical Market Price

Mortality Projection on Indonesia's Abridged Life Table to Determine the EPV of Term Annuity

Estimation of present value of whole life annuity using information about expectation of life

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