Modelling of an insurance premium through the application of actuarial methods, failure theory and Black-Scholes in the health in Colombia
DOI:
https://doi.org/10.46661/revmetodoscuanteconempresa.5800Keywords:
insurance premium, actuarial studies, individual risk model, collective risk model, failure rate, credibility theory, valuation of financial assets, aggregate claim amountAbstract
The pricing’s premium in an insurance for the health sector is influenced by the claims ratio of its subscribers, which generates high levels of fluctuation and uncertainty. The objective of this research is the application of the actuarial individual risk models, collective risk and credibility model, together with the application of the failure rate technological model and the Black-Scholes financial options model as tools for estimating pricing’s premium for the insurance and health industry in Colombia. Based on the claims and the total costs of the historical claims, the models are applied to ensure optimal premiums for coverage of the aggregate losses of the claims. In the end, comparing these models and approaching a definition of an optimal method. The importance of the research settles in the high commitment, responsibility and financial impact of managing and mitigating the impact of actuarial risk, proposing new methodologies through an optimal estimation level in premiums to certify proper functioning of the sector entities in matters of costs, sustainability and service compliance in the sector.
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References
Black, F., & Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of political economy, 81(3), 637-654. https://doi.org/10.1086/260062
Bühlmann, H. (1969). Experience rating and credibility. ASTIN Bulletin: The Journal of the IAA, 5(2), 157-165. https://doi.org/10.1017/S0515036100008023
Chen, Y., Cheung, K.C., Choi, H.M., & Yam, S. C. (2020). Evolutionary credibility risk premium. Insurance: Mathematics and Economics, 93, 216-229. https://doi.org/10.1016/j.insmatheco.2020.04.015
Committee on Ratemaking Principles (Mayo de 1988). Statement of Principles Regarding Property and Casualty Insurance Ratemaking. https://www.casact.org/education/spring/2012/handouts%5CSession_5134_handout_401_0.pdf
Cossette, H., Marceau, E., & Mtalai, I. (2019). Collective risk models with dependence. Insurance: Mathematics and Economics, 87, 153-168. https://doi.org/10.1016/j.insmatheco.2019.04.008
Denuit, M.M., Kiriliouk, A., & Segers, J. (2015). Max-factor individual risk models with application to credit portfolios. Insurance: Mathematics and Economics, 62, 162-172. https://doi.org/10.1016/j.insmatheco.2015.03.006
Efron, B., & Gong, G. (1983). A Leisurely Look at the Bootstrap, the Jackknife, and Cross-Validation. The American Statistician, 37(1), 36-48. https://doi.org/10.1080/00031305.1983.10483087
Finger, R.L. (2001). Risk Classification. En Foundations of Casualty Actuarial (4th ed., pp. 287-342). Casualty Actuarial Society.
Fisher, R.A. (1955). Statistical Methods and Scientific Induction. Journal of the Royal Statistical Society, 17(1), 69-78. https://doi.org/10.1111/j.2517-6161.1955.tb00180.x
Garrido, J., & Genest, C. (2016). Generalized linear models for dependent frequency and severity of insurance claims. Insurance: Mathematics and Economics, 70, 205-215. https://doi.org/10.1016/j.insmatheco.2016.06.006
Gulumser, M., Tonkin, R.S., & Johannes, D.J. (2002). Competition in the general insurance industry. Zeitschrift für die gesamte Versicherungswissenschaft, 91(3), 453-481. https://doi.org/10.1007/BF03190772
Hua, L. (2015). Tail negative dependence and its applications for aggregate loss. Mathematics and Economics, 61, 135-145. https://doi.org/10.1016/j.insmatheco.2015.01.001
Jeong, H., & Valdez, E.A. (2020). Predictive compound risk models with dependence. Insurance: Mathematics and Economics, 94, 182-195. https://doi.org/10.1016/j.insmatheco.2020.07.011
Jiang, R. (2013). A new bathtub curve model with a finite support. Reliability Engineering & System Safety, 119, 44-51. https://doi.org/10.1016/j.ress.2013.05.019
Klugman, S.A., Panjer, H.H., & Willmot, G. E. (2008). Loss Models. From Data to Decisions (3th ed.). Hoboken, New Jersey: Jhon Wiley & Sons, Inc. https://doi.org/10.1002/9780470391341
Klugman, S.A., Panjer, H. H., & Willmot, G.E. (2019). Loss Models: From Data to Decisions (5th ed.). New Jersey: John Wiley and Sons, Inc.
Lamothe, P., & Pérez, M. (2005). Opciones financieras y productos estructurados (3th ed.). Madrid: McGraw-Hill Interamericana.
Lee, G.Y., & Shi, P. (2019). A dependent frequency-severity approach to modeling longitudinal insurance claims. Insurance: Mathematics and Economics, 87, 115-129. https://doi.org/10.1016/j.insmatheco.2019.04.004
Lenhard, J. (2006). Models and Statistical Inference: The Controversy between Fisher and Neyman-Pearson. The British Journal for the Philosophy of Science, 57(1), 69-91. https://doi.org/10.1093/bjps/axi152
Marín, J.M., & Rubio, G. (2001). Economía financiera. Antoni Bosch editor.
Martel, M., Hernández, A., & Vázquez, F.J. (2012). On the independence between risk profiles in the compound collective risk actuarial model. Mathematics and Computers in Simulation, 82(8), 1419-431. https://doi.org/10.1016/j.matcom.2012.01.003
Migon, H.S., & Moura, F.A. (2005). Hierarchical Bayesian collective risk model: an application to health insurance. Insurance: Mathematics and Economics, 36(2), 119-135. https://doi.org/10.1016/j.insmatheco.2004.11.006
Miller, R. B., & Hickman, J.C. (1975). Teoría de la credibilidad del seguro y estimación bayesiana. Teoría y aplicaciones de la credibilidad, 249-270.
Minsalud. (2020). Estudio de suficiencia y de los mecanismos de ajuste del riesgo para el cálculo de la Unidad de Pago por Capitación, recursos para garantizar la financiación de tecnologías en salud y servicios en los regímenes Contributivo y Subsidiado. Colombia: Ministerio de la Salud.
Monterrey, P. (2012). P<0,05, ¿Criterio mágico para resolver cualquier problema o leyenda urbana? Universidad Javeriana, 17(2), 203-215. https://doi.org/10.11144/javeriana.SC17-2.pamc
Moreno, M.T., & Ramos, L. (2003). Aplicación de Modelos de Credibilidad para el Cálculo de Primas en el Seguro de Automóviles. Comisión Nacional de Seguros y Fianzas de los Estados Unidos Mexicanos.
Mudholkar, G.S., Asubonteng, K.O., & Hutson, A.D. (2009). Transformation of the bathtub failure rate data in reliability for using Weibull-model analysis. Statistical Methodology, 6(6), 622-633. https://doi.org/10.1016/j.stamet.2009.07.003
Norberg, R. (1979). The credibility approach to experience rating. Scandinavian Actuarial Journal, 4, 181-221. https://doi.org/10.1080/03461238.1979.10413721
OCDE. (2016). Principios de Gobierno Corporativo de la OCDE y del G20. (p. 68). Paris: OCDE. http://dx.doi.org/10.1787/9789264259171-es
Parodi, P. (2015). Pricing in General Insurance (Vol. 10). New York: Chapman and Hall. https://doi.org/10.1201/b17525
Roesch, W. J. (2012). Using a new bathtub curve to correlate quality and reliability. Microelectronics Reliability, 52(12), 2864-2869. https://doi.org/10.1016/j.microrel.2012.08.022
Roos, B. (2007). On variational bounds in the compound Poisson approximation of the individual risk model. Insurance: Mathematics and Economics, 40(3), 403-414. https://doi.org/10.1016/j.insmatheco.2006.06.003
Shreve, S.E. (2004). Stochastic calculus for finance II: Continuous-time models (Vol. 11). New York: Springer. https://doi.org/10.1007/978-1-4757-4296-1
Schinzinger, E., Denuit, M.M., & Christiansen, M.C. (2016). A multivariate evolutionary credibility model for mortality improvement rates. Insurance: Mathematics and Economics, 69, 70-81. https://doi.org/10.1016/j.insmatheco.2016.04.004
Tsai, C.C.-L., & Wu, A.D. (2020). Incorporating hierarchical credibility theory into modelling of multi-country mortality rates. Insurance: Mathematics and Economics, 91, 37-54. https://doi.org/10.1016/j.insmatheco.2020.01.001
Wen, L., Wu, X., & Zhou, X. (2009). The credibility premiums for models with dependence induced by common effects. Insurance: Mathematics and Economics, 44(1), 19-25. https://doi.org/10.1016/j.insmatheco.2008.09.005
Werner, G., & Modlin, C. (2019). Basic Ratemaking. Casualty Actuarial Society.
Xie, M., Tang, Y., & Goh, T. N. (2002). A modified Weibull extension with bathtub-shaped failure rate function. Reliability Engineering & System Safety, 76(3), 279-285. https://doi.org/10.1016/S0951-8320(02)00022-4
Yang, J., Zhou, S., & Zhang, Z. (2005). The compound Poisson random variable's approximation to the individual risk model. Insurance: Mathematics and Economics, 36(1), 57-77. https://doi.org/10.1016/j.insmatheco.2004.10.003
Yeo, K.L., & Valdez, E.A. (2006). Claim dependence with common effects in credibility models. Insurance: Mathematics and Economics, 38(2), 609-629. https://doi.org/10.1016/j.insmatheco.2005.12.006
Zhang, T., Xie, M., Tang, L.C., & NG, S.H. (2005). Reliability and modeling of systems integrated with firm ware and hard ware. International Journal of Reliability, Quality and Safety Engineering, 12(3), 227-339. https://doi.org/10.1142/S021853930500180X
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