PENDEKATAN BAYESIAN MARKOV CHAIN MONTE CARLO (MCMC) METROPOLIS-HASTINGS PADA PEMODELAN KLAIM ASURANSI KESEHATAN

Aprida Siska Lestia; Mochammad Idris

doi:10.20527/epsilon.v18i2.13872

PENDEKATAN BAYESIAN MARKOV CHAIN MONTE CARLO (MCMC) METROPOLIS-HASTINGS PADA PEMODELAN KLAIM ASURANSI KESEHATAN

Aprida Siska Lestia, Mochammad Idris

Abstract

The distribution of health insurance claims that tend to be asymmetric and have heavy tails, requires a method that can offer more flexible and robust solutions than traditional frequentist approaches, such as the Bayesian Method. The advantage of this method lies in its ability to comprehensively account for uncertainty in parameter estimation, thereby producing a posterior distribution that can capture complex pattern of claim data. This study aims to apply the Bayesian approach with the Markov Chain Monte Carlo (MCMC) Metropolis-Hastings method in modeling health insurance claims. The claim data used are divided into outpatient and inpatient claims, with the lognormal distribution fitting proven to be the most appropriate for both types of claims. Risk estimation through Value at Risk (VaR) and Conditional Tail Expectation (CTE) using the Bayesian approach showed more moderate results compared to empirical estimates, indicating that this approach can reduce risk overestimation

Keywords

Health Insurance Claim, Bayesian, MCMC, Metropolis-Hastings

Full Text:

PDF

References

Artzner P., Delbaen, F., Eber, J. M., & Heath D. (1999). Coherent measures of risk. Math. Finance. Vol. 9(3), 203–228.

https://doi.org/https://doi.org/10.1111/1467-9965.00068

Diana, E. N., & Soehardjoepri. (2016). Pendekatan Metode Bayesian untuk Kajian Estimasi Parameter Distribusi Log-Normal untuk Non-Informatif Prior. Jurnal Sains Dan Seni ITS. Vol. 5(2), A14–A16.

https://doi.org/https://dx.doi.org/10.12962/j23373520.v5i2.16468

Facchinett, S. (2009). A Procedure to Find Exact Critical Values of Kolmogorov-Smirnov Test. Italian Journal of Applied Statistics. Vol. 21, 337–359.

Fitriani, R., & Gunardi. (2020). Implementasi Metode Bayes pada perhitungan Premi Asuransi Kendaraan Bermotor. Journal of Fundamental Mathematics and Applications (JFMA). Vol. 3(2), 112–123.

https://doi.org/10.14710/jfma.v3i2.8257

Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2013). Bayesian Data Analysis (3rd Edition). Chapman and Hall Press.

Klugman, S. A., Panjer, H. H., & Willmot, G. E. (2019). Loss Models from Data to Decisions (5th ed.). John Wiley and Sons, Inc. www.wiley.com

Lestia, A. S. (2021). Model Risiko (Vol. 1). CV. Banyubening Cipta Sejahtera.

Lestia, A. S., & Tampubolon, D. R. (2016). Capital-Based Risk Measures For Some Probability Models. Proceedings of International Conference on NAMES 2015, Faculty of Mathematics and Natural Sciences. 217–224.

Markov, U. E. (2013). Principal applications of Bayesian methods in actuarial science. North American Actuarial Journal. Vol. 5(4), 53–57.

https://doi.org/10.1080/10920277.2001.10596011

McNeil, A. J., Frey, R., & Embrechts, P. (2015). Quantitative Risk Management: Concepts, Techniques, and Tools (Revised Edition). Princeton University Press.

Migon, H. S., & Penna, E. M. O. (2006). Bayesian Analysis of a Health Insurance Model. Journal of Actuarial Practice. Vol. 13, 60–80.

Rezaei, M., & Malekjani, M. (2021). Comparison between different methods of model selection in cosmology. The European Physical Journal Plus. Vol. 136(2), 219.

https://doi.org/10.1140/epjp/s13360-021-01200-w

Robert, C. P. (2015). The Metropolis–Hastings Algorithm. In Wiley StatsRef: Statistics Reference Online. 1–15. Wiley.

https://doi.org/10.1002/9781118445112.stat07834

Robert, C. P., & Casella, G. (2004). Monte Carlo Statistical Methods (2nd Edition). Springer.

Speagle, J. S. (2019). A Conceptual Introduction to Markov Chain Monte Carlo Methods. Harvard & Smithsonian Center for Astrophysics., arXiv-1909.

Sukono, Riaman, Lesmana, E., Wulandari, R., Napitupulu, H., & Supian, S. (2018). Model estimation of claim risk and premium for motor vehicle insurance by using Bayesian method. IOP Conference Series: Materials Science and Engineering. Vol. 300(1).

https://doi.org/10.1088/1757-899X/300/1/012027

Sukono, Suyudi, M., Islamiyati, F., & Supian, S. (2017). Estimation model of life insurance claims risk for cancer patients by using Bayesian method. IOP Conference Series: Materials Science and Engineering. Vol. 166(1).

https://doi.org/10.1088/1757-899X/166/1/012022

Tse, Y. K. (2014). Nonlife Actuarial Models Theory, Methods and Evaluation. United States of America by Cambridge University Press.

DOI: https://doi.org/10.20527/epsilon.v18i2.13872