Actuarial Measures for Inverse Gaussian Distributed Claim Severity
DOI:
https://doi.org/10.20956/j.v20i2.30067Keywords:
Inverse Gaussian Distribution, Kolmogorov-Smirnov Method, Maximum Likelihood, Value at RiskAbstract
An insurance company must be able to manage risks in the form of claims submitted by policyholders. There are several risk measures or actuarial measures that can be used to predict future risks and help companies prepare reserves. These actuarial measures are Value at Risk (VaR), Tail Value at Risk (TVaR), Tail Variance (TV), and Tail Variance Premium (TVP). In this article, we will discuss these actuarial measures for inverse Gaussian distributed claim severity. The Kolmogorov-Smirnov test is used to test the fit of the inverse Gaussian distribution. The maximum likelihood estimator is used as a method to estimate the parameters of the inverse Gaussian distribution. The data used in this article is data on partial loss claims for motor vehicle insurance insurance company PT. ABC in 2019 Category 1 in all regions. However, after testing the goodness of fit of the distribution using the Kolmogorov-Smirnov test for region 3, it did not come from a population with an inverse Gaussian distribution. So the data used to proceed to the actuarial measures estimation stage is only region 1 and region 2. Based on the results of calculating the actuarial measures for inverse Gaussian distributed claim severity, it can be concluded that the value of losses expected by a company can be calculated by taking into account the actuarial measures for claim severity on motor vehicle insurance in Indonesia.
References
Ahmad, Z., Mahmoudi, E., Hamedani, G. G., & Kharazmi, O., 2020. New Methods to Define Heavy-Tailed Distributions with Applications to Insurance Data. Journal of Taibah University For Science, Vol. 14, No. 1, Hal. 359-382.
Chhikara, R. S. & Folks, J. L., 1978. The Inverse Gaussian Distribution and its StatisticalApplication—A Review. J. R. Statist. Soc. B, 40, No. 3, pp. 263-289
Eini, E. J. & Khaloozadeh, H., 2020. Tail Variance for Generalized Skew-Elliptical Distributions. Journal Taylor & Francis Online, Vol. 51, Issue. 2.
Furman, E. & Landsman, Z., 2006. Tail Variance Premium With Applications for Elliptical Portofolio of Risks. Artikel. Astin Bulletin 36(2):433-462.
Putri, I. & Syuhada, K. I. A., 2017. Ukuran Risiko Cre-VaR. Prosiding Seminar Nasional Metode Kuantitatif. ISBN No.978-602-98559-3-7.
Mutaqin, A. K., 2001. Distribusi Inverse Gaussian Sebagai Salah Satu Distribusi Kegagalan. Jurnal Statistika Unisba Vol.1, No.1.
Sukmayani, S. P., 2015. Analisis Pengukuran Risiko Menggunakan Generalized Pareto Distribution Pada Klaim Asuransi Jiwa PT. Y. Surabaya
Zhao, J., Ahmad, Z., Mahmoudi, E., Hafez, E. H., & El-Din, M. M. M., 2021. A New Class of Heavy-Tailed Distributions: Modeling and Simulating Actuarial Measures. Journal of Hindawi Complexity, Vol. 2021, Article ID 5580228, Hal. 18.
Downloads
Published
Issue
Section
License
Copyright (c) 2023 Author and publisher
This work is licensed under a Creative Commons Attribution 4.0 International License.
This work is licensed under a Creative Commons Attribution 4.0 International License.
Jurnal Matematika, Statistika dan Komputasi is an Open Access journal, all articles are distributed under the terms of the Creative Commons Attribution License, allowing third parties to copy and redistribute the material in any medium or format, transform, and build upon the material, provided the original work is properly cited and states its license. This license allows authors and readers to use all articles, data sets, graphics and appendices in data mining applications, search engines, web sites, blogs and other platforms by providing appropriate reference.
