Stochastic Interest Rate Approach of Pricing Participating Life Insurance Policies with Embedded Surrender Option

Mustapha Abdul-Rahaman; Francis Oduro; Al-Hassan Issahaku

doi:doi:10.11648/j.ajmcm.20180301.12

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Stochastic Interest Rate Approach of Pricing Participating Life Insurance Policies with Embedded Surrender Option

Mustapha Abdul-Rahaman, Francis Oduro, Al-Hassan Issahaku

Published in American Journal of Mathematical and Computer Modelling (Volume 3, Issue 1)

Received: 15 February 2018 Accepted: 9 March 2018 Published: 8 April 2018

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Abstract

Life insurance contracts are priced and analysed using techniques from actuarial and modern financial mathematics, which requires that, the conditions for the risk-neutral valuation are fulfilled and that, a specified underlying security and an equivalent martingale measure must exist. This paper analysed life insurance endowment policy, paid by sequence of periodical premiums in Ghana with a guaranteed minimum return to the policyholder. Again, this paper presents two premium determination schemes for the insurance policy, the constant premium case and the periodical adjustment case in which both the benefit and the periodical premiums are annually adjusted in relation to the performance of a reference portfolio. It was realized that, with rising guaranteed interest rate, the rate of return on the reference portfolio, the premiums of the whole contract decreased both in the constant and the periodical adjustment cases whiles an increase in the participating coefficient and age of the insured led to an increase in the whole premium both in the constant and periodical adjustment cases. Also, it was revealed that, the premium of the non-surrendered bonus option is smaller in the constant premium case than in the periodical adjustment case and the premium of the bonus option in the surrendered participating policy looks cheap in the constant premium case than in the periodical adjustment case. Thus, it’s about 1.03% and 6.95% respectively of the total premium for the constant and for the periodical adjustment cases.

Published in	American Journal of Mathematical and Computer Modelling (Volume 3, Issue 1)
DOI	10.11648/j.ajmcm.20180301.12
Page(s)	10-21
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), 2018. Published by Science Publishing Group

Keywords

Stochastic Interest Rate, Surrender Option, Participating Policies, Life Insurance Policy, Periodical Premiums

References

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APA Style

Mustapha Abdul-Rahaman, Francis Oduro, Al-Hassan Issahaku. (2018). Stochastic Interest Rate Approach of Pricing Participating Life Insurance Policies with Embedded Surrender Option. American Journal of Mathematical and Computer Modelling, 3(1), 10-21. https://doi.org/10.11648/j.ajmcm.20180301.12

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ACS Style

Mustapha Abdul-Rahaman; Francis Oduro; Al-Hassan Issahaku. Stochastic Interest Rate Approach of Pricing Participating Life Insurance Policies with Embedded Surrender Option. Am. J. Math. Comput. Model. 2018, 3(1), 10-21. doi: 10.11648/j.ajmcm.20180301.12

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AMA Style

Mustapha Abdul-Rahaman, Francis Oduro, Al-Hassan Issahaku. Stochastic Interest Rate Approach of Pricing Participating Life Insurance Policies with Embedded Surrender Option. Am J Math Comput Model. 2018;3(1):10-21. doi: 10.11648/j.ajmcm.20180301.12

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@article{10.11648/j.ajmcm.20180301.12,
  author = {Mustapha Abdul-Rahaman and Francis Oduro and Al-Hassan Issahaku},
  title = {Stochastic Interest Rate Approach of Pricing Participating Life Insurance Policies with Embedded Surrender Option},
  journal = {American Journal of Mathematical and Computer Modelling},
  volume = {3},
  number = {1},
  pages = {10-21},
  doi = {10.11648/j.ajmcm.20180301.12},
  url = {https://doi.org/10.11648/j.ajmcm.20180301.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmcm.20180301.12},
  abstract = {Life insurance contracts are priced and analysed using techniques from actuarial and modern financial mathematics, which requires that, the conditions for the risk-neutral valuation are fulfilled and that, a specified underlying security and an equivalent martingale measure must exist. This paper analysed life insurance endowment policy, paid by sequence of periodical premiums in Ghana with a guaranteed minimum return to the policyholder. Again, this paper presents two premium determination schemes for the insurance policy, the constant premium case and the periodical adjustment case in which both the benefit and the periodical premiums are annually adjusted in relation to the performance of a reference portfolio. It was realized that, with rising guaranteed interest rate, the rate of return on the reference portfolio, the premiums of the whole contract decreased both in the constant and the periodical adjustment cases whiles an increase in the participating coefficient and age of the insured led to an increase in the whole premium both in the constant and periodical adjustment cases. Also, it was revealed that, the premium of the non-surrendered bonus option is smaller in the constant premium case than in the periodical adjustment case and the premium of the bonus option in the surrendered participating policy looks cheap in the constant premium case than in the periodical adjustment case. Thus, it’s about 1.03% and 6.95% respectively of the total premium for the constant and for the periodical adjustment cases.},
 year = {2018}
}

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TY  - JOUR
T1  - Stochastic Interest Rate Approach of Pricing Participating Life Insurance Policies with Embedded Surrender Option
AU  - Mustapha Abdul-Rahaman
AU  - Francis Oduro
AU  - Al-Hassan Issahaku
Y1  - 2018/04/08
PY  - 2018
N1  - https://doi.org/10.11648/j.ajmcm.20180301.12
DO  - 10.11648/j.ajmcm.20180301.12
T2  - American Journal of Mathematical and Computer Modelling
JF  - American Journal of Mathematical and Computer Modelling
JO  - American Journal of Mathematical and Computer Modelling
SP  - 10
EP  - 21
PB  - Science Publishing Group
SN  - 2578-8280
UR  - https://doi.org/10.11648/j.ajmcm.20180301.12
AB  - Life insurance contracts are priced and analysed using techniques from actuarial and modern financial mathematics, which requires that, the conditions for the risk-neutral valuation are fulfilled and that, a specified underlying security and an equivalent martingale measure must exist. This paper analysed life insurance endowment policy, paid by sequence of periodical premiums in Ghana with a guaranteed minimum return to the policyholder. Again, this paper presents two premium determination schemes for the insurance policy, the constant premium case and the periodical adjustment case in which both the benefit and the periodical premiums are annually adjusted in relation to the performance of a reference portfolio. It was realized that, with rising guaranteed interest rate, the rate of return on the reference portfolio, the premiums of the whole contract decreased both in the constant and the periodical adjustment cases whiles an increase in the participating coefficient and age of the insured led to an increase in the whole premium both in the constant and periodical adjustment cases. Also, it was revealed that, the premium of the non-surrendered bonus option is smaller in the constant premium case than in the periodical adjustment case and the premium of the bonus option in the surrendered participating policy looks cheap in the constant premium case than in the periodical adjustment case. Thus, it’s about 1.03% and 6.95% respectively of the total premium for the constant and for the periodical adjustment cases.
VL  - 3
IS  - 1
ER  -

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Author Information

Mustapha Abdul-Rahaman

Department of Mathematics, Kwame Nkrumah University of Science and Technology, Kumasi, Ghana
Francis Oduro

Department of Mathematics, Kwame Nkrumah University of Science and Technology, Kumasi, Ghana
Al-Hassan Issahaku

Department of Informatics, Regent University College of Science and Technology, Accra, Ghana

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Plain Text BibTeX RIS

APA Style

Mustapha Abdul-Rahaman, Francis Oduro, Al-Hassan Issahaku. (2018). Stochastic Interest Rate Approach of Pricing Participating Life Insurance Policies with Embedded Surrender Option. American Journal of Mathematical and Computer Modelling, 3(1), 10-21. https://doi.org/10.11648/j.ajmcm.20180301.12

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ACS Style

Mustapha Abdul-Rahaman; Francis Oduro; Al-Hassan Issahaku. Stochastic Interest Rate Approach of Pricing Participating Life Insurance Policies with Embedded Surrender Option. Am. J. Math. Comput. Model. 2018, 3(1), 10-21. doi: 10.11648/j.ajmcm.20180301.12

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AMA Style

Mustapha Abdul-Rahaman, Francis Oduro, Al-Hassan Issahaku. Stochastic Interest Rate Approach of Pricing Participating Life Insurance Policies with Embedded Surrender Option. Am J Math Comput Model. 2018;3(1):10-21. doi: 10.11648/j.ajmcm.20180301.12

Copy | Download

@article{10.11648/j.ajmcm.20180301.12,
  author = {Mustapha Abdul-Rahaman and Francis Oduro and Al-Hassan Issahaku},
  title = {Stochastic Interest Rate Approach of Pricing Participating Life Insurance Policies with Embedded Surrender Option},
  journal = {American Journal of Mathematical and Computer Modelling},
  volume = {3},
  number = {1},
  pages = {10-21},
  doi = {10.11648/j.ajmcm.20180301.12},
  url = {https://doi.org/10.11648/j.ajmcm.20180301.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmcm.20180301.12},
  abstract = {Life insurance contracts are priced and analysed using techniques from actuarial and modern financial mathematics, which requires that, the conditions for the risk-neutral valuation are fulfilled and that, a specified underlying security and an equivalent martingale measure must exist. This paper analysed life insurance endowment policy, paid by sequence of periodical premiums in Ghana with a guaranteed minimum return to the policyholder. Again, this paper presents two premium determination schemes for the insurance policy, the constant premium case and the periodical adjustment case in which both the benefit and the periodical premiums are annually adjusted in relation to the performance of a reference portfolio. It was realized that, with rising guaranteed interest rate, the rate of return on the reference portfolio, the premiums of the whole contract decreased both in the constant and the periodical adjustment cases whiles an increase in the participating coefficient and age of the insured led to an increase in the whole premium both in the constant and periodical adjustment cases. Also, it was revealed that, the premium of the non-surrendered bonus option is smaller in the constant premium case than in the periodical adjustment case and the premium of the bonus option in the surrendered participating policy looks cheap in the constant premium case than in the periodical adjustment case. Thus, it’s about 1.03% and 6.95% respectively of the total premium for the constant and for the periodical adjustment cases.},
 year = {2018}
}

Copy | Download

TY  - JOUR
T1  - Stochastic Interest Rate Approach of Pricing Participating Life Insurance Policies with Embedded Surrender Option
AU  - Mustapha Abdul-Rahaman
AU  - Francis Oduro
AU  - Al-Hassan Issahaku
Y1  - 2018/04/08
PY  - 2018
N1  - https://doi.org/10.11648/j.ajmcm.20180301.12
DO  - 10.11648/j.ajmcm.20180301.12
T2  - American Journal of Mathematical and Computer Modelling
JF  - American Journal of Mathematical and Computer Modelling
JO  - American Journal of Mathematical and Computer Modelling
SP  - 10
EP  - 21
PB  - Science Publishing Group
SN  - 2578-8280
UR  - https://doi.org/10.11648/j.ajmcm.20180301.12
AB  - Life insurance contracts are priced and analysed using techniques from actuarial and modern financial mathematics, which requires that, the conditions for the risk-neutral valuation are fulfilled and that, a specified underlying security and an equivalent martingale measure must exist. This paper analysed life insurance endowment policy, paid by sequence of periodical premiums in Ghana with a guaranteed minimum return to the policyholder. Again, this paper presents two premium determination schemes for the insurance policy, the constant premium case and the periodical adjustment case in which both the benefit and the periodical premiums are annually adjusted in relation to the performance of a reference portfolio. It was realized that, with rising guaranteed interest rate, the rate of return on the reference portfolio, the premiums of the whole contract decreased both in the constant and the periodical adjustment cases whiles an increase in the participating coefficient and age of the insured led to an increase in the whole premium both in the constant and periodical adjustment cases. Also, it was revealed that, the premium of the non-surrendered bonus option is smaller in the constant premium case than in the periodical adjustment case and the premium of the bonus option in the surrendered participating policy looks cheap in the constant premium case than in the periodical adjustment case. Thus, it’s about 1.03% and 6.95% respectively of the total premium for the constant and for the periodical adjustment cases.
VL  - 3
IS  - 1
ER  -

Copy | Download