Implementation of Gaussian Process Regression in Estimating Motor Vehicle Insurance Claims Reserves

Ria Novita Suwandani; Yogo  Purwono

doi:10.47616/jamrems.v2i1.77

Autori

Ria Novita Suwandani Master of Actuarial Management, Faculty of Economics and Business, University of Indonesia
Yogo Purwono Master of Actuarial Management, Faculty of Economics and Business, University of Indonesia

DOI:

https://doi.org/10.47616/jamrems.v2i1.77

Parole chiave:

Claims Reserves, Gaussian Process Regression, Motor Vehicle Insurance

Abstract

This study aims to calculate the allowance for losses by applying Gaussian Process regression to estimate future claims. Modeling is done on motor vehicle insurance data. The data used in this study are historical data on PT XYZ's motor vehicle insurance business line during 2017 and 2019 (January 2017 to December 2019). Data analysis will be carried out on the 2017 - 2019 data to obtain an estimate of the claim reserves in the following year, namely 2018 - 2020. This study uses the Chain Ladder method which is the most popular loss reserving method in theory and practice. The estimation results show that the Gaussian Process Regression method is very flexible and can be applied without much adjustment. These results were also compared with the Chain Ladder method. Estimated claim reserves for PT XYZ's motor vehicle business line using the chain-ladder method, the company must provide funds for 2017 of 8,997,979,222 IDR in 2018 16,194,503,605 IDR in 2019 amounting to Rp. 1,719,764,520 for backup. Meanwhile, by using the Bayessian Gaussian Process method, the company must provide funds for 2017 of 9,060,965,077 IDR in 2018 amounting to 16,307,865,130 IDR, and in 2019 1,731,802,871 IDR for backup. The more conservative Bayessian Gaussian Process method. Motor vehicle insurance data has a short development time (claims occur) so that it is included in the short-tail type of business.

Downloads

I dati di download non sono ancora disponibili.

Riferimenti bibliografici

Antonio, K., Beirlant, J., Hoedemakers, T & Verlaak, R. (2006). Lognormal mixed models for reported claim reserve. North American Actuarial Journal 10(1),30–48.

Barber, D. (2012). Bayesian reasoning and machine learning. Cambridge University Press.

BPS. (2019). Perkembangan Jumlah Kendaraan Bermotor Menurut Jenis, 1949-2018. https://www.bps.go.id/linkTableDinamis/view/id/1133

Brown, J. R., & Goolsbee, A. (2002). Does the Internet make markets more competitive? Evidence from the life insurance industry. Journal of political economy, 110(3), 481-507.

de Alba, E., & Nieto-Barajas, L. E. (2008). Claims reserving: a correlated Bayesian model. Insurance: Mathematics and Economics, 43(3), 368-376.

Friedland, F., & Chasan, M. B. (2010). U.S. Patent Application No. 12/258,559.

Gigante, P., Picech, L & Sigalotti, L. (2013). Prediction error for credible claims reserves: an h-likelihood approach. European Actuarial Journal, 3(2),453-470.

Giraud, W. J., Kingsbury, B. D., Rasmussen, M. H., & Rodriguez, D. (2016). U.S. Patent No. 9,519,118. Washington, DC: U.S. Patent and Trademark Office.

Hudecová, Š., & Pešta, M. (2013). Modeling dependencies in claims reserving with GEE. Insurance: Mathematics and Economics, 53(3), 786-794.

Hürlimann, W. (2009) Credible loss ratio claims reserves: The Benktander, Neuhaus and Mack methods revisited. Astin Bulletin, 39(01).

Jedlicka, P. (2007). Various extensions based on Munich Chain Ladder method. In ASTIN Colloquium, Orlando, Florida, http://www. actuaries. org/ASTIN/Colloquia/Orlando/Presentations/Jedlicka. pdf.

Lally, N., & Hartman, B. (2018). Estimating loss reserves using hierarchical Bayesian Gaussian process regression with input warping. Insurance: Mathematics and Economics, 82, 124-140.

Larhed, M., & Olofsson, K. (Eds.). (2006). Microwave methods in organic synthesis (Vol. 266). Springer.

Mack, R., & Nielsen, J. (1993). Usability inspection methods: Report on a workshop held at CHI'92, Monterey, CA, May 3–4, 1992. ACM Sigchi Bulletin, 25(1), 28-33.

Martínez-Miranda, M. D., Nielsen, J. P., & Verrall, R. J. (2012). Double chain ladder. Astin Bulletin, 42(1), 59-76.

Shi, P., & Hartman, B. M. (2016). Credibility in loss reserving. North American Actuarial Journal, 20(2), 114-132.

Snoek, J., Swersky, K., Zemel, R., & Adams, R. (2014, June). Input warping for bayesian optimization of non-stationary functions. In International Conference on Machine Learning (pp. 1674-1682). PMLR.

Taylor, G., McGuire, G., & Greenfield, A. (2003). Loss reserving: past, present and future. University of Melbourne Centre of Actuarial Studies Research Paper, (109).

Wüthrich, M.V & Merz, M. (2008). Stochastic Claims Reserving Methods in Insurance. In: Wiley Finance Series, John Wiley & Sons.