Actuarial Modeling of COVID-19 Insurance

Mila Kurniawaty, Maulana Muhamad Arifin, Bagus Kurniawan, Sadam Laksamana Sukarno, Muhammad Teguh Prayoga

Abstract


In this article, we provide an actuarial model expected to be able to help financial arrangements to cover losses due to the outbreak of coronavirus disease (COVID-19). We construct the dynamical models of premium and benefit based on generalized SEIR (Susceptible-Exposed-Infected-Recovered). Based on its dynamical model, we formulate the premium and the premium reserves on hospitalization and death benefits of the COVID-19 insurance.


Keywords


premium; premium reserves; generalized SEIR; hospitalization benefit; death benefit

Full Text:

PDF

References


C. Huang, Y. Wang, X. Li, L. Ren, J. Zhao, Y. Hu, Li. Zhang, G. Fan, J. Xu, X. Gu, Z. Cheng, T. Yu, J. Xia, Y. Wei, W. Wu, X. Xie, W. Yin, H. Li, M. Liu, Y. Xiao, H. Gao, L. Guo, J. Xie, G. Wang, R. Jiang, Z. Gao, Q. Jin, J. Wang, and B. Cao. Clinical features of patients infected with 2019 novel coronavirus in Wuhan, China. The Lancet, vol.395, Issue 10223, pp. 497-506, 2020.

M. F. Sattar, S. Khanum, A. Nawaz, M. M. Ashfaq, M. A. Khan, M. Jawad, and W. Ullah. Covid-19 Global, Pandemic impact on World Economy. Technium Social Sciences Journal. vol. 11, pp.165-179, 2020.

A. Arfah, F. Z. Olilingo, F. Zain, S. Syaifuddin, D. Dahliah, N. Nurmiati, and A. H. K. P.Putra. Economics During Global Recession: Sharia-Economics as a Post COVID-19 Agenda. Journal of Asian Finance, Economic and Business, vol.7, no. 11, pp.1077-1085, 2020.

R. Feng and J. Garrido. Actuarial Applications of Epidemiological Models. North American Actuarial Journal, vol. 15, no.1, pp. 112-136, 2012.

H. U. Gerber. Life Insurance Mathematics. Springer, Berlin, Heidelberg, 1997.

M. Batista. Estimation of the Final Size of The Coronavirus Epidemic by the SIR Model, preprint, 2020.

I. Cooper, A. Mondal, and C. G. Antonopoulos. A SIR Model Assumption For The Spread Of COVID-19 In Different Communities. Chaos, Solitons and Fractals, vol. 139, 2020.

B. Tang, N.L. Bragazzi, Q. Li, S. Tang, Y. Xiao, and J. Wu, J. An updated estimation of the risk of transmission of the novel coronavirus (2019-nCoV). Infectious Disease Modelling. vol. 5, pp. 248-255, 2020.

T. Zhou, Q. Liu, Z. Yang, J. Liao, K. Yang, W. Bai, X. Lu, and W. Zhang. Preliminary predistion of the basic reproduction number of the Wuhan novel coronavirus 2019-nCoV. Journal of Evidence-based Medicine, vol. 13, no.1, 2020.

B. L. Jones. Actuarial Calculations Using a Markov Model. Transactions of the Society of Actuaries, vol. 46, pp.227–250, 1994.

N. Jia and L. Tsui. Epidemic Modelling using SARS as a Case Study. North American Actuarial Journal, vol. 9, no.4, pp. 28 – 42, 2005.

Canadian Institute of Actuaries, “Considerations for the Development of a Pandemic Scenario”. Canadian Institute of Actuaries, Committee on Risk Management and Capital Requirements. Research Paper 209095, 2009.

L. Peng, W. Yang, D. Zhang, C. Zhuge, and L. Hong. Epidemic analysis of COVID19 in China by dynamical modeling. arXiv preprint arXiv:2002.06563, 2020.

D. Aldila, S. H. A. Khoshnaw, E. Safitri, Y. R. Anwar, A. R. Q. Bakry, B. M. Samiadji, D. A. Anugerah, M. F. Alfarizi, I. D. Ayulani, and S. N. Salim. A mathematical study on the spread of COVID-19 considering social distancing and rapid assessment: The case of Jakarta, Indonesia. Chaos, Solitons and Fractals, vol.139, 2020.

Woldometer. Report coronavirus cases. Retrieved March 17, 2021, from https://www.worldometers.info/coronavirus/#countries, 2021.

N. L. Bowers, H. U. Gerber, J. C. Hickman, D A. Jones, and C. J. Nesbitt. Actuarial Mathematics. The Society of Actuaries, 1997.

R. J. Cunningham, T. N. Herzog, and R. L. London. Model fo Quantifying Risk, 2nd ed, ACTEX Publication Inc., Winsted, 2006.

D. C. M. Dickson, M. R. Hardy, and H. R. Waters. Actuarial Mathematics for Life Contingent Risks, 2nd ed, Cambridge University Press, United Kingdom, 2003.

R. K. Sembiring. Buku Materi Pokok Asuransi I. Karunika Universitas Terbuka. Jakarta, 1986.

I. Catarya. Buku Materi Pokok Asuransi II. Karunika Universitas Terbuka. Jakarta, 1988.




DOI: https://doi.org/10.18860/ca.v7i3.14999

Refbacks

  • There are currently no refbacks.


Copyright (c) 2022 Mila Kurniawaty, Maulana Muhamad Arifin, Bagus Kurniawan, Sadam Laksamana Sukarno, Muhammad Teguh Prayoga

Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Editorial Office
Mathematics Department,
Universitas Islam Negeri Maulana Malik Ibrahim Malang
Gajayana Street 50 Malang, East Java, Indonesia 65144
Faximile (+62) 341 558933
e-mail: cauchy@uin-malang.ac.id

Creative Commons License
CAUCHY: Jurnal Matematika Murni dan Aplikasi is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.