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Abstract
The 2019 Indonesian Mortality Table IV (TMI IV) involved 52 life insurance companies in Indonesia during the study period from 2013 to 2017. From the data, there may be differences in the characteristics of company customers so that the use of TMI IV is not in accordance with these characteristics. In life insurance companies, there are types of coverage (causes), namely: NDPA, which means death due to illness or accident; PAD, which means reimbursement of medical expenses, and SRD, which is the cancellation of the policy so that the coverage ends. The Companies can construct a Life Table involving multiple causes called a Multiple Decrement (MD) Table. This table is modified into a Modified Multiple Decrement Table (MDT) by adding factors to the causes in the form of regions. The clustering of factors needs to be done to reduce the complexity of the calculation. Using the K-means method, the grouping of regions R1R9 is divided into the following: PAD causes (3 groups) and SRD (2 groups). MDT is obtained from the relationship between MD and the Associated Single Decrement (ASD). The Annual Exposure Method was used to calculate the probability of causes. Furthermore, extrapolation is performed on the probability of cause, for which there is no value, and graduation is performed on the less smooth probability of cause. Then, credibility theory is used to determine the credibility level of the industry. The industry-credible probability of cause has a value between the observed value and the industry value (TMI IV).
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References
- Bowers, N. L., Gerber, H. U., Hickman, J. C., Jones, D. A., and Nesbitt, C. J., Actuarial Mathematics, Society of Actuaries, 1997.
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- Christiansen, M. C., and Denuit, M. M., Worst-case actuarial calculations consistent with single-and multiple-decrement life tables, Insurance: Mathematics and Economics, 52(2) (2013), 1-5.
- Luptkov, I. D., and Bilkov, M, Actuarial modeling of life insurance using decrement models, Journal of Applied Mathematics, Statistics and Informatics, 10(1) (2014), 81-91.
- Lee, H., Ahn, J. Y., and Ko, B., Construction of multiple decrement tables under generalized fractional age assumptions, Computational Statistics & Data Analysis, 133 (2019), 104-119.
- Debicka, J., and Zmyslona, B., A Multiple State Model for Premium Calculation when Several Premium-Paid States are Involved, Central European Journal of Economic Modelling and Econometrics, (2018), 27-52.
- Jang, J., and Mohd Ramli, S. N., Hierarchical Markov model in life insurance and social benefit schemes, Risks, 6, (2018), 63.
- Sirin, I., A multiple decrement life table model for orphan daughters in Turkey, Journal of Statisticians: Statistics and Actuarial Sciences, 13, (2020), 48-60.
- Lee, H., Ha, H., and Lee, T., Decrement rates and a numerical method under competing risks, Computational Statistics & Data Analysis, 156, (2021), 107125.
- Deshmukh, S. R., Multiple decrement models in insurance: an introduction using R, Springer Science & Business Media, 2012.
- Agusta, Y., K-means: Penerapan, permasalahan dan metode terkait, Jurnal Sistem dan informatika, 3(1) (2007), 47-60.
- Vendramin, L., Campello, R. J., and Hruschka, E. R., ”On the comparison of relative clustering validity criteria”, In Proceedings of the 2009 SIAM international conference on data mining (2009), 733-744
References
Bowers, N. L., Gerber, H. U., Hickman, J. C., Jones, D. A., and Nesbitt, C. J., Actuarial Mathematics, Society of Actuaries, 1997.
Biswas, S., Grover, G., and Varshney, M. K., A Method of Construction a Multiple Increment Decrement Life Table of HIV Population, International Journal of Medical and Biological Frontiers, 17(3) (2011), 187.
Arthur, E. K., and Obayemi, J. D., Modification of a Multiple Decrement Model and Its Significance: A case study of Northern Ghana, International Journal of Probability and Statistics, 2(2) (2013), 21-27.
Christiansen, M. C., and Denuit, M. M., Worst-case actuarial calculations consistent with single-and multiple-decrement life tables, Insurance: Mathematics and Economics, 52(2) (2013), 1-5.
Luptkov, I. D., and Bilkov, M, Actuarial modeling of life insurance using decrement models, Journal of Applied Mathematics, Statistics and Informatics, 10(1) (2014), 81-91.
Lee, H., Ahn, J. Y., and Ko, B., Construction of multiple decrement tables under generalized fractional age assumptions, Computational Statistics & Data Analysis, 133 (2019), 104-119.
Debicka, J., and Zmyslona, B., A Multiple State Model for Premium Calculation when Several Premium-Paid States are Involved, Central European Journal of Economic Modelling and Econometrics, (2018), 27-52.
Jang, J., and Mohd Ramli, S. N., Hierarchical Markov model in life insurance and social benefit schemes, Risks, 6, (2018), 63.
Sirin, I., A multiple decrement life table model for orphan daughters in Turkey, Journal of Statisticians: Statistics and Actuarial Sciences, 13, (2020), 48-60.
Lee, H., Ha, H., and Lee, T., Decrement rates and a numerical method under competing risks, Computational Statistics & Data Analysis, 156, (2021), 107125.
Deshmukh, S. R., Multiple decrement models in insurance: an introduction using R, Springer Science & Business Media, 2012.
Agusta, Y., K-means: Penerapan, permasalahan dan metode terkait, Jurnal Sistem dan informatika, 3(1) (2007), 47-60.
Vendramin, L., Campello, R. J., and Hruschka, E. R., ”On the comparison of relative clustering validity criteria”, In Proceedings of the 2009 SIAM international conference on data mining (2009), 733-744