Private Premium of Endowment Last Survivor and Joint Life Insurance with Pareto Distribution

Hasriati; Tumpal Parulian Nababan

doi:doi:10.11648/j.ijsd.20190504.11

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Private Premium of Endowment Last Survivor and Joint Life Insurance with Pareto Distribution

Hasriati, Tumpal Parulian Nababan

Received: 7 October 2019 Accepted: 4 November 2019 Published: 8 November 2019

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Abstract

This paper studies a dual life insurance premium is determined with the combined status of last survivor and joint life involving two insurance participants who have a kinship relationship such as husband and wife, brother and sister, which they work in the same agency. In determining the policy to be made by the life insurance does not require two policies to be made, but enough to have only one policy. So that by having one policy expected premiums paid by life insurance participants to life insurance companies will be smaller than if you have to pay in two policies. Determination of insurance premiums dual life to be paid by an insurance party participant based on the chance of death from both life insurance participants, stating a condition that will continue as long as there is at least one member who is still alive and will cease after the death of the last person of its member, and also is an ongoing condition se long time all members of a combination of several people can survive and will stop after one of its members first dies, to determine the single premium and annual premium using the cash value of the initial life annuity from dual life insurance. Whereas the initial annuity cash value is influenced by the interest rate and discount factor and is also influenced by the combined life opportunity of the two insurance participants. Furthermore, from the chance of life will be obtained the chance of dying In formulating the chance of dying the insurance participant is used the Pareto distribution and to obtain the parameter values in the Pareto distribution the maximum Likelihood method is used. In order to obtain the chance of death and can be used to calculate a single premium and annual premium.

DOI	10.11648/j.ijsd.20190504.11
Published in	International Journal of Statistical Distributions and Applications (Volume 5, Issue 4, December 2019)
Page(s)	76-81
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Premi, Last Survivor, Joint Life, Distribusi Pareto, Maksimum Likelihood

References

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[3]	D. C. M. Dickson, M. R. Hardy dan H. R. Waters. (2009) Actuarial Mathematics for Life Contingent Risk, Cambridge University Press, Cambridge.
[4]	M. B. Finan, A Reading of Life Contingency Model: A Preparation for Exam MLC/3L, Arkansas Teach University, Arkansas, 2011.
[5]	T. Futami. (1993). Matematika Asuransi Jiwa, Bagian I, Terj. Seimei Hoken Sugaku, Gekan (92 Revision), oleh G. Herliyanto. Oriental Life Insurane Cultural Development Center. Tokyo.
[6]	T. Futami. (1994). Matematika Asuransi Jiwa, Bagian II, Terj. Seimei Hoken Sugaku, Gekan (92 Revision), oleh G. Herliyanto. Oriental Life Insurane Cultural Development Center. Tokyo.
[7]	Heekyung Youn, Arkady Shemyakin, Edwin Herman, (2002). A Re-examination of Joint Mortality Functions, North Amirican Actuarial Journal Volume 6, Number 1, p. 166-170.
[8]	A. Jhon dan L. Albert. (2016). “Actuarial Analysis of Single Life Status and Multiple Life Statuses”. American Journal of Theoretical and Applied Statistics 2016; 5 (3); 123-131.
[9]	S. G. Kellison. (1991). The Theory of Interest. Richard D. Irwin Inc, Homewood.
[10]	A. Matvejevs dan A. Matvejevs, (2001) Insurance models for joint life and last survivor nenefits, Informatica, 12, 547-558.
[11]	Robert Musian, (2003). Mathematics of Interest Rate, Insurance, Social Security, and Pensiuns Prentice-Hall, London.
[12]	Roger J, Gray and Susan M. Pitts, (2012) Risk Modelling in General Insurance, International Series on Actuarial Science, Cambridge Universitas Press.
[13]	M. Rytgaard. (1990). “Estimation in the Pareto distribution”. Astin Bulletin 1990; 20; 202-216.
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[16]	Youn, H and Shemyakin, A. (2001). Pricing Practices for Joint Last Survivor Insurance, Actuarial Research Clearing House.

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APA Style

Hasriati, Tumpal Parulian Nababan. (2019). Private Premium of Endowment Last Survivor and Joint Life Insurance with Pareto Distribution. International Journal of Statistical Distributions and Applications, 5(4), 76-81. https://doi.org/10.11648/j.ijsd.20190504.11

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ACS Style

Hasriati; Tumpal Parulian Nababan. Private Premium of Endowment Last Survivor and Joint Life Insurance with Pareto Distribution. Int. J. Stat. Distrib. Appl. 2019, 5(4), 76-81. doi: 10.11648/j.ijsd.20190504.11

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AMA Style

Hasriati, Tumpal Parulian Nababan. Private Premium of Endowment Last Survivor and Joint Life Insurance with Pareto Distribution. Int J Stat Distrib Appl. 2019;5(4):76-81. doi: 10.11648/j.ijsd.20190504.11

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@article{10.11648/j.ijsd.20190504.11,
  author = {Hasriati and Tumpal Parulian Nababan},
  title = {Private Premium of Endowment Last Survivor and Joint Life Insurance with Pareto Distribution},
  journal = {International Journal of Statistical Distributions and Applications},
  volume = {5},
  number = {4},
  pages = {76-81},
  doi = {10.11648/j.ijsd.20190504.11},
  url = {https://doi.org/10.11648/j.ijsd.20190504.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijsd.20190504.11},
  abstract = {This paper studies a dual life insurance premium is determined with the combined status of last survivor and joint life involving two insurance participants who have a kinship relationship such as husband and wife, brother and sister, which they work in the same agency. In determining the policy to be made by the life insurance does not require two policies to be made, but enough to have only one policy. So that by having one policy expected premiums paid by life insurance participants to life insurance companies will be smaller than if you have to pay in two policies. Determination of insurance premiums dual life to be paid by an insurance party participant based on the chance of death from both life insurance participants, stating a condition that will continue as long as there is at least one member who is still alive and will cease after the death of the last person of its member, and also is an ongoing condition se long time all members of a combination of several people can survive and will stop after one of its members first dies, to determine the single premium and annual premium using the cash value of the initial life annuity from dual life insurance. Whereas the initial annuity cash value is influenced by the interest rate and discount factor and is also influenced by the combined life opportunity of the two insurance participants. Furthermore, from the chance of life will be obtained the chance of dying In formulating the chance of dying the insurance participant is used the Pareto distribution and to obtain the parameter values in the Pareto distribution the maximum Likelihood method is used. In order to obtain the chance of death and can be used to calculate a single premium and annual premium.},
 year = {2019}
}

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TY  - JOUR
T1  - Private Premium of Endowment Last Survivor and Joint Life Insurance with Pareto Distribution
AU  - Hasriati
AU  - Tumpal Parulian Nababan
Y1  - 2019/11/08
PY  - 2019
N1  - https://doi.org/10.11648/j.ijsd.20190504.11
DO  - 10.11648/j.ijsd.20190504.11
T2  - International Journal of Statistical Distributions and Applications
JF  - International Journal of Statistical Distributions and Applications
JO  - International Journal of Statistical Distributions and Applications
SP  - 76
EP  - 81
PB  - Science Publishing Group
SN  - 2472-3509
UR  - https://doi.org/10.11648/j.ijsd.20190504.11
AB  - This paper studies a dual life insurance premium is determined with the combined status of last survivor and joint life involving two insurance participants who have a kinship relationship such as husband and wife, brother and sister, which they work in the same agency. In determining the policy to be made by the life insurance does not require two policies to be made, but enough to have only one policy. So that by having one policy expected premiums paid by life insurance participants to life insurance companies will be smaller than if you have to pay in two policies. Determination of insurance premiums dual life to be paid by an insurance party participant based on the chance of death from both life insurance participants, stating a condition that will continue as long as there is at least one member who is still alive and will cease after the death of the last person of its member, and also is an ongoing condition se long time all members of a combination of several people can survive and will stop after one of its members first dies, to determine the single premium and annual premium using the cash value of the initial life annuity from dual life insurance. Whereas the initial annuity cash value is influenced by the interest rate and discount factor and is also influenced by the combined life opportunity of the two insurance participants. Furthermore, from the chance of life will be obtained the chance of dying In formulating the chance of dying the insurance participant is used the Pareto distribution and to obtain the parameter values in the Pareto distribution the maximum Likelihood method is used. In order to obtain the chance of death and can be used to calculate a single premium and annual premium.
VL  - 5
IS  - 4
ER  -

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Author Information

Hasriati

Department of Mathematics, Faculty of Mathematics and Natural Sciences, University of Riau, Pekanbaru, Indonesia
Tumpal Parulian Nababan

Department of Mathematics, Faculty of Mathematics and Natural Sciences, University of Riau, Pekanbaru, Indonesia

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APA Style

Hasriati, Tumpal Parulian Nababan. (2019). Private Premium of Endowment Last Survivor and Joint Life Insurance with Pareto Distribution. International Journal of Statistical Distributions and Applications, 5(4), 76-81. https://doi.org/10.11648/j.ijsd.20190504.11

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ACS Style

Hasriati; Tumpal Parulian Nababan. Private Premium of Endowment Last Survivor and Joint Life Insurance with Pareto Distribution. Int. J. Stat. Distrib. Appl. 2019, 5(4), 76-81. doi: 10.11648/j.ijsd.20190504.11

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AMA Style

Hasriati, Tumpal Parulian Nababan. Private Premium of Endowment Last Survivor and Joint Life Insurance with Pareto Distribution. Int J Stat Distrib Appl. 2019;5(4):76-81. doi: 10.11648/j.ijsd.20190504.11

Copy | Download

@article{10.11648/j.ijsd.20190504.11,
  author = {Hasriati and Tumpal Parulian Nababan},
  title = {Private Premium of Endowment Last Survivor and Joint Life Insurance with Pareto Distribution},
  journal = {International Journal of Statistical Distributions and Applications},
  volume = {5},
  number = {4},
  pages = {76-81},
  doi = {10.11648/j.ijsd.20190504.11},
  url = {https://doi.org/10.11648/j.ijsd.20190504.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijsd.20190504.11},
  abstract = {This paper studies a dual life insurance premium is determined with the combined status of last survivor and joint life involving two insurance participants who have a kinship relationship such as husband and wife, brother and sister, which they work in the same agency. In determining the policy to be made by the life insurance does not require two policies to be made, but enough to have only one policy. So that by having one policy expected premiums paid by life insurance participants to life insurance companies will be smaller than if you have to pay in two policies. Determination of insurance premiums dual life to be paid by an insurance party participant based on the chance of death from both life insurance participants, stating a condition that will continue as long as there is at least one member who is still alive and will cease after the death of the last person of its member, and also is an ongoing condition se long time all members of a combination of several people can survive and will stop after one of its members first dies, to determine the single premium and annual premium using the cash value of the initial life annuity from dual life insurance. Whereas the initial annuity cash value is influenced by the interest rate and discount factor and is also influenced by the combined life opportunity of the two insurance participants. Furthermore, from the chance of life will be obtained the chance of dying In formulating the chance of dying the insurance participant is used the Pareto distribution and to obtain the parameter values in the Pareto distribution the maximum Likelihood method is used. In order to obtain the chance of death and can be used to calculate a single premium and annual premium.},
 year = {2019}
}

Copy | Download

TY  - JOUR
T1  - Private Premium of Endowment Last Survivor and Joint Life Insurance with Pareto Distribution
AU  - Hasriati
AU  - Tumpal Parulian Nababan
Y1  - 2019/11/08
PY  - 2019
N1  - https://doi.org/10.11648/j.ijsd.20190504.11
DO  - 10.11648/j.ijsd.20190504.11
T2  - International Journal of Statistical Distributions and Applications
JF  - International Journal of Statistical Distributions and Applications
JO  - International Journal of Statistical Distributions and Applications
SP  - 76
EP  - 81
PB  - Science Publishing Group
SN  - 2472-3509
UR  - https://doi.org/10.11648/j.ijsd.20190504.11
AB  - This paper studies a dual life insurance premium is determined with the combined status of last survivor and joint life involving two insurance participants who have a kinship relationship such as husband and wife, brother and sister, which they work in the same agency. In determining the policy to be made by the life insurance does not require two policies to be made, but enough to have only one policy. So that by having one policy expected premiums paid by life insurance participants to life insurance companies will be smaller than if you have to pay in two policies. Determination of insurance premiums dual life to be paid by an insurance party participant based on the chance of death from both life insurance participants, stating a condition that will continue as long as there is at least one member who is still alive and will cease after the death of the last person of its member, and also is an ongoing condition se long time all members of a combination of several people can survive and will stop after one of its members first dies, to determine the single premium and annual premium using the cash value of the initial life annuity from dual life insurance. Whereas the initial annuity cash value is influenced by the interest rate and discount factor and is also influenced by the combined life opportunity of the two insurance participants. Furthermore, from the chance of life will be obtained the chance of dying In formulating the chance of dying the insurance participant is used the Pareto distribution and to obtain the parameter values in the Pareto distribution the maximum Likelihood method is used. In order to obtain the chance of death and can be used to calculate a single premium and annual premium.
VL  - 5
IS  - 4
ER  -

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