http://doi.org/10.35668/2520-6524-2025-2-02
Huseynova Arzu D. — D. Sc. in Economics, Professor, First Deputy Chairman of the Board, The Economic Scientific Research Institute of the Ministry of Economy of the Republic of Azerbaijan (ESRI), 196 Hasan bay Zardabi, Yasamal, Baku, Azerbaijan AZ1122; Azerbaijan State University of Economics (UNEC), Azerbaijan Technical University (AzTU), Baku, Azerbaijan, arzu.huseynova@esri.gov.az; ORCID: 0000-0002-0981-9923
Hasanova Afet — Doctoral student, The Economic Scientific Research Institute of the Ministry of Economy of the Republic of Azerbaijan (ESRI), 196 Hasan bay Zardabi, Yasamal, Baku, Azerbaijan AZ1122; afet.hesenova@gmail.com; ORCID: 0009-0008-7836-4337
CALCULATION OF INSURANCE PREMIUM RESERVES FOR LIFE INSURANCE AND APPLICATION OF THE ZILLMER METHOD AGAINST NEGATIVE RESULTS IN THE FIRST YEAR
Abstract. The purpose of this article is to examine the application of the Zillmer method to mitigate or eliminate the negative reserve that arises during the first year when expenses are charged to the insurance premium reserves calculated for life insurance. The net premium reserve for whole life insurance and term insurance types has been calculated using both prospective and retrospective methods. The formulas for calculating the actuarial present value of insurance payments (paid), life annuities, and premiums, which are the main components of the insurance premium reserve, as well as substitution decrements and commutation functions, are provided. Expenses affecting the reserve are classified as initial expenses (α), collection expenses (β), and administrative expenses (γ). The methodology for converting net premium reserves into gross premium reserves by charging the α, β, and γ expenses is presented. Various approaches of the Zillmer method have been analyzed to address the negative premium reserve that arises in the first year when the commission, which is part of the initial expense (α), is added.
Keywords: life insurance, prospective and retrospective methods, initial expense, annuity, net premium reserve, Zillmer method.
REFERENCES
- Akdeniz, F., & Erdugan, F. (2014). Aktüerya Matematiği ve Yaşam Analizi. Özyurt Matbaacılık, 2, Baskı, Akademisyen Yayınevi.
- Al Ghifari, Y., & Sudding, F. N. F. (2023). Analysis of Premium Reserve Using Zillmer Method and Canadian Method for Endowment Joint Life Insurance. Journal of Actuarial, Finance, and Risk Management, 2(1), 28-32.
- August, (1989). August Zillmer, an actuary with less reserve. Journal Society of Actuaries, 23(3), 8-9. Retrieved from: The Actuary Vol. 23, No. 3 August Zillmer, An Actuary With Less Reserve.
- Gerber, H. U. (2013). Life İnsurance Mathematics. Third Edition. Springer Science & Business Media. 224 DOI: 10.1007/978-3-662-03460-6.
- Məmtiyev, T. R. (2020). Həyat sığortası riyaziyyatı. Bakı. s. 725.
- Promislow, S. D. (2014). Fundamentals of actuarial mathematics. Third Edition. John Wiley & Sons, 554 p. Retrieved from: https://www.actuariayfinanzas.net/images/sampledata/FundamentalsofActuarialMathematics_S.DavidPromislow2015.pdf.
- Rachman, M. I., & Pertiwi, A. D. (2022). Comparison of Zillmer and Premium Sufficiency Reserve Method using the Vasicek Stochastic Interest Rate Model. Journal Matematika Integratif, 18 (2), 189-202.
- Reisnanda, A., Subartini, B., & Riaman, R. (2024). Comparison of the Zillmer Method with the Adjusted Ohio Method in Calculation of Premium Reserve Value in Dwi-Purpose Life Insurance. International Journal of Quantitative Research and Modeling, 5 (1), 49-54.
- Setianingsih, D., & Rosita, S. (2024). Modıfıcatıon of prospectıve lıfe ınsurance reserve prospectıve calculatıons usıng the Zıllmer method. Journal of Mathematical Sciences and Optimization, 1 (2), 63-71.
- Council directive of 19 Desemder 1991 (91/674/EEC). Official Journal of The European Communities, L, 24 p. Retrieved from: eur-lex.europa.eu/legal-content/EN/TXT/PDF/?uri=CELEX:31991L0674.
