LOSS ELIMINATION RATIO OF TOTAL MOTOR VEHICLE INSURANCE LOSSES USING ORDINARY DEDUCTIBLE

Authors

  • Berlian Setiawaty IPB University
  • Mutiara Maharani IPB University
  • Ruhiyat Ruhiyat IPB University
  • Windiani Erliana IPB University

DOI:

https://doi.org/10.25077/jmua.14.1.1-13.2025

Keywords:

loss elimination ratio, ordinary deductible, simulasi Monte Carlo, total kerugian

Abstract

Penelitian ini membahas total kerugian dari asuransi kendaraan bermotor jika diterapkan ordinary deductible. Data yang digunakan dalam penelitian ini adalah data Motorcycle Insurance dari package insuranceData R. Pemodelan total kerugian dilakukan dengan memodelkan banyak klaim menggunakan sebaran binomial negatif dan besar klaim menggunakan sebaran beta-prime. Sebaran total kerugian merupakan sebaran compound dengan sebaran primernya binomial negatif dan sebaran sekundernya beta-prime. Sebaran compound ini sulit diperoleh bentuk analitiknya sehingga digunakan simulasi Monte Carlo. Dengan simulasi Monte Carlo dapat dihitung nilai harapan kerugian agregat tanpa ordinary deductible maupun dengan ordinary deductible, sehingga diperoleh loss elimination ratio dari penggunaan ordinary deductible. Dari perhitungan yang dilakukan dapat disimpulkan semakin besar nilai ordinary deductible, semakin meningkat pula loss elimination ratio-nya.

References

Klugman, SA., Panjer, HH., Willmot, GE.,2019, Loss Models: From Data to Decisions, Edisi ke-5, John Wiley and Sons, Inc., Hoboken NJ, USA

Gray, RJ., Pitts, SM., 2012, Risk Modelling in General Insurance, Edisi ke-1, Cambridge University Press, Cambridge, UK

Poufinas, T., Gogas, P., Papadimitriou, T., Zaganidis, 2023, Machine learning in forecasting motor insurance claims, Risks Vol. 11(9): 164. https://doi.org/10.3390/risks11090164

Ohlsson, E., Johansson, B., 2010, Non-life insurance pricing with generalized linear models, Springer, Berlin, Heidelberg.

Lee, GY., Frees, EW., 2016, General Isurance Deductible Ratemaking with Applications to the Local Government Property Insurance Fund. https://www.soa.org/globalassets/assets/Files/Research/Projects/research-2016-gi-deductible-ratemaking.pdf

Mohamed, MA., Ahmad, MR., Noriszura, I., 2010, Approximation of aggregate losses using simulation, Journal of Mathematics and Statistics, 6(3): 233 – 239

Shevchenko, PV., 2010, Calculation of aggregate loss distributions, The Journal of Operational Risk, 5(2) : 3 – 40

Tulupyev, A., Suvorovava, A., Sousa, J., Zelterman, D. 2013, Beta prime regression with application to risky behaviour frequency screening, Stat. Med, 32 (23): 4044 – 4056

Montgomery, DC., 2001, Design and Analysis of Experiments, 5th ed, John Wiley and Sons, New York

Feller, W., 1948, On the Kolmogorov-Smirnov limit theorems for empirical distributions, The Annals of Mathematical Statistics, 19(2): 177 – 189. doi:10.1214/aoms/1177730243

Marsaglia, G., Tsang, WW., Wang, L., 2003, Evaluating Kolmogorov’s distribution, Journal of Statistical Software, 8(18).doi:10.18637/jss.v008.i18

Ghahramani, S., 2005, Fundamentals of Probability with Stochastic Processes, Edisi ke-3, Prentice Hall, New Jersey, US.

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Published

31-01-2025

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