Araştırma Makalesi
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Yıl 2023, Sayı: 39, 161 - 171, 27.12.2023

Övgücan Karadağ Erdemir

Öz

Kaynakça

  • Abdelhadi, S., Elbahnasy, K. & Abdelsalam, M. (2020). A Proposed Model to Predict Auto Insurance Claims Using Machine Learning Techniques. Journal of Theoretical and Applied Information Technology, 98(22). google scholar
  • Alpaydin, E. (2020). Introduction to machine learning. MIT press. google scholar
  • Arvidsson, H. & Francke, S. (2007). Dependence in Non-Life Insurance. UUDM Project Report. 0 google scholar
  • Baldacchino, T., Cross, E.J., Worden, K. & Rowson, J. (2016). Variational Bayesian Mixture of Experts Models and Sensitivity Analysis for Nonlinear Dynamical Systems. Mechanical Systems and Signal Processing, 66, 178-200. google scholar
  • Boateng, M.A., Omari-Sasu, A.Y., Avuglah, R.K. & Frempong, N.K. (2017). On Two Random Variables and Archimedean Copulas. International Journal of Statistics and Applications, 7(4), 228. google scholar
  • Czado, C., Kastenmeier, R., Brechmann E.C. & Min, A. (2012). A Mixed Copula Model for Insurance Claims and Claim Sizes. Scandinavian Actuarial Journal, 4, 278. google scholar
  • Dempster, A.P., Laird, N.M. & Rubin, D.B. (1977). Maximum Likelihood from Incomplete Data via the EM Algorithm. Journal of the Royal Statistical Society, Series B (Methodological), 39, 1-38. google scholar
  • Dewi, K.C., Murfi, H. & Abdullah, S. (2019). Analysis Accuracy of Random Forest Model for Big Data-A Case Study of Claim Severity Prediction in Car Insurance. 5th International Conference on Science in Information Technology (ICSITech), 60-65. google scholar
  • Emekliler, N.A. (2017). Karayolları Motorlu Araçlar Zorunlu Mali Sorumluluk Sigortasında Hasar Oranlarının Hesaplanması ve Hasar Oranlarının Tahmini Emekliler Sigorta Örneği. Master Dissertation in Turkish, Başkent Üniversitesi Sosyal Bilimler Enstitüsü, Turkey. google scholar
  • Erdemir, Ö.K. & Sucu, M. (2022). A Modified Pseudo-Copula Regression Model for Risk Groups with Various Dependency Levels. Journal of Statistical Computation and Simulation, 92(5), 1092-1112. google scholar
  • Eryılmaz, S. (2017). On Compound Sums Under Dependency. Insurance: Mathematics and Economics, 72, 228. google scholar
  • Frees, E.W., Myers G. & David, C. (2010). Dependent Multi-peril Ratemaking Models. ASTIN Bulletin, 40, 699. google scholar
  • Garrido, J., Genest, C. & Schulz, J. (2016). Generalized Linear Models for Dependent Frequency and Severity of Insurance Claims. Insurance: Mathematics and Economics, 70, 205. google scholar
  • Hanafy, M. & Ming, R. (2021). Machine Learning Approaches for Auto Insurance Big Data. Risks, 9(2), 42. google scholar
  • Hastie, T., Tibshirani, R., Friedman, J. H., & Friedman, J. H. (2009). The elements of statistical learning: data mining, inference, and prediction (Vol. 2, pp. 1-758). New York: springer. google scholar
  • Hu, S., Murphy, T.B. & O’Hagan, A. (2019). Bivariate Gamma Mixture of Experts Models for Joint Insurance Claims Modelling. Cornell University, arXiv: arxiv.org/abs/1904.04699. google scholar
  • Hu, S., Murphy, T.B. & O’Hagan, A. (2021). MvClaim: An R Package for Multivariate General Insurance Claims Severity Modelling. Annals of Actuarial Science, 15(2), 441-457. google scholar
  • Jeong, H., Valdez, E. A., Ahn, J. Y. & Park, S. (2017). Generalized Linear Mixed Models for Dependent Compound Risk Models. SSRN 3045360. google scholar
  • Klugman, S.A., Panjer, H.H. & Willmot, G.E. (2012). Loss models: from data to decisions. John Wiley & Sons, 715. google scholar
  • Kramer, N., Brechmann, E.C., Silvestrini, D. & Czado, C. (2013). Total Loss Estimation Using Copula-Based Regression Models. Insurance: Mathematics and Economics, 53, 829. google scholar
  • Masarotto, G. & Varin, C. (2017). Gaussian Copula Regression in R. Journal of Statistical Software, 77 (8). google scholar
  • Murphy, K. P. (2012). Machine learning: a probabilistic perspective. MIT press. google scholar
  • Nelsen, R.B. (2007). An Introduction to Copulas. Springer science & business media. google scholar
  • Parsa R.A. & Klugman, S.A. (2011). Copula Regression. Variance Advancing and Science of Risks, 5, 45. google scholar
  • Purhadi, B. & Purnami, S. (2018). Parameter Estimation and Statistical Test in Bivariate Gamma Regression Model. 8th Annual Basic Science Onternational Conference. google scholar
  • Ren, J. (2012). A Multivariate Aggregate Loss Model. Insurance: Mathematics and Economics, 51, 402. google scholar
  • Singh, R., Ayyar, M.P., Pavan, T.V.S., Gosain, S. & Shah, R.R. (2019). Automating Car Insurance Claims Using Deep Learning Techniques. google scholar
  • IEEE fifth international conference on multimedia big data (BigMM), 199-207. google scholar
  • Sklar, A. (1959). Fonctions de repartition a n dimensions et leurs marges. Publications de l’Institut Statistique de l’Universite de Paris, 8, 229-231. google scholar
  • Song, P.X.K (2007). Correlated Data Analysis: Modeling, Analytics, And Applications. Springer Science & Business Media, Ontario, Canada. google scholar
  • Song, P.X.-K., Li, M. & Yuan, Y. (2009). Joint Regression Analysis of Correlated Data Using Gaussian Copulas. Biometrics, 65(1), 60-68. google scholar
  • Su, J. & Furman, E. (2017). A Form of Multivariate Pareto Distribution with Applications to Financial Risk Measurement. ASTIN Bulletin: The Journal of the IAA, 47(1), 331-357. google scholar
  • Şahin, Ş., Nevruz, E., Karageyik, B. B., & Simsek, G. (2020). Destekten Yoksun Kalma Tazminatı Hesaplama Yöntemleri, Şeçkin Yayıncılık, Türkiye. google scholar
  • Şahin, Ş., Karageyik, B. B., Nevruz, E., & Simsek, G. (2021). Aktüerya Bilirkişiliği-İş Göremezlik Tazminatı Hesaplama Yöntemleri, Şeçkin Yayıncılık, Türkiye. google scholar
  • Tatlidil, H. (1996). Uygulamalı Çok Degiskenli İstatistiksel Analiz. Cem Web Ofset Ltd. Sti, Ankara. google scholar
  • Vernic, R. (2000). A Multivariate Generalization of The Generalized Poisson Distribution. ASTIN Bulletin, 30(1), 57-67. google scholar
  • Vernic, R., Bolance, C. & Alemany, R. (2022). Sarmanov Distribution for Modeling Dependence Between the Frequency and the Average Severity of Insurance Claims. Insurance: Mathematics and Economics, 102, 111-125. google scholar
  • Weerasinghe, K.P.M.L.P. & Wijegunasekara, M.C. (2016). A Comparative Study of Data Mining Algorithms in The Prediction of Auto Insurance Claims. European International Journal of Science and Technology, 5(1), 47-54. google scholar
  • Yolal, H.E. (2019). Karayolları Motorlu Araçlar Zorunlu Mali Sorumluluk (Trafik) Sigortalarında Sigorta Tazminatının Ödenmesinde Kusurun Etkisi. ProQuest Dissertations & Theses Global. google scholar
  • Zadeh, A. H. & Bilodeau, M. (2013). Fitting Bivariate Losses with Phase-Type Distributions. Scandinavian Actuarial Journal, 4, 241. google scholar
  • https://www.tsb.org.tr/tr/istatistikler Access date: 06.04.2023 google scholar
  • https://www.tsb.org.tr/media/attachments/Trafik_Genel_%C5%9Eartlar%C4%B1_06122021__Ekler_Dahil.pdf,Trafik Sigortası Genel Şartları, Access date: 21.08.2023 google scholar

A Comparative Perspective on Multivariate Modeling of Insurance Compensation Payments with Regression-Based and Copula-Based Models

Yıl 2023, Sayı: 39, 161 - 171, 27.12.2023

Övgücan Karadağ Erdemir

Öz

In this study, compensation payments for Turkish motor vehicles’ compulsory third-party liability insurance between 2018 and 2022 are modeled from a comparative perspective using regression-based and copula-based multivariate statistical methods. The assumption of gamma distribution for logarithmic compensation payment variables is carried out in both approaches. Bivariate gamma regression is established using the bivariate gamma distribution, and the mixture of experts, one of the machine learning techniques, is employed to form the mixture of bivariate gamma regressions. The bivariate copula regression and finite mixture of copula regression models are designed using the Gumbel and Frank copula functions. The computational analyses were conducted using the mvClaim package in R. Based on the comparison of model results, a mixture of copula-based models is found to be more suitable for the multivariate modeling of insurance compensation payments.

Anahtar Kelimeler

Bivariate Gamma Distribution Copula Generalized Linear Model Copula Regression Insurance Compensation Payments Machine Learning Techniques Mixture of Experts Model

Kaynakça

  • Abdelhadi, S., Elbahnasy, K. & Abdelsalam, M. (2020). A Proposed Model to Predict Auto Insurance Claims Using Machine Learning Techniques. Journal of Theoretical and Applied Information Technology, 98(22). google scholar
  • Alpaydin, E. (2020). Introduction to machine learning. MIT press. google scholar
  • Arvidsson, H. & Francke, S. (2007). Dependence in Non-Life Insurance. UUDM Project Report. 0 google scholar
  • Baldacchino, T., Cross, E.J., Worden, K. & Rowson, J. (2016). Variational Bayesian Mixture of Experts Models and Sensitivity Analysis for Nonlinear Dynamical Systems. Mechanical Systems and Signal Processing, 66, 178-200. google scholar
  • Boateng, M.A., Omari-Sasu, A.Y., Avuglah, R.K. & Frempong, N.K. (2017). On Two Random Variables and Archimedean Copulas. International Journal of Statistics and Applications, 7(4), 228. google scholar
  • Czado, C., Kastenmeier, R., Brechmann E.C. & Min, A. (2012). A Mixed Copula Model for Insurance Claims and Claim Sizes. Scandinavian Actuarial Journal, 4, 278. google scholar
  • Dempster, A.P., Laird, N.M. & Rubin, D.B. (1977). Maximum Likelihood from Incomplete Data via the EM Algorithm. Journal of the Royal Statistical Society, Series B (Methodological), 39, 1-38. google scholar
  • Dewi, K.C., Murfi, H. & Abdullah, S. (2019). Analysis Accuracy of Random Forest Model for Big Data-A Case Study of Claim Severity Prediction in Car Insurance. 5th International Conference on Science in Information Technology (ICSITech), 60-65. google scholar
  • Emekliler, N.A. (2017). Karayolları Motorlu Araçlar Zorunlu Mali Sorumluluk Sigortasında Hasar Oranlarının Hesaplanması ve Hasar Oranlarının Tahmini Emekliler Sigorta Örneği. Master Dissertation in Turkish, Başkent Üniversitesi Sosyal Bilimler Enstitüsü, Turkey. google scholar
  • Erdemir, Ö.K. & Sucu, M. (2022). A Modified Pseudo-Copula Regression Model for Risk Groups with Various Dependency Levels. Journal of Statistical Computation and Simulation, 92(5), 1092-1112. google scholar
  • Eryılmaz, S. (2017). On Compound Sums Under Dependency. Insurance: Mathematics and Economics, 72, 228. google scholar
  • Frees, E.W., Myers G. & David, C. (2010). Dependent Multi-peril Ratemaking Models. ASTIN Bulletin, 40, 699. google scholar
  • Garrido, J., Genest, C. & Schulz, J. (2016). Generalized Linear Models for Dependent Frequency and Severity of Insurance Claims. Insurance: Mathematics and Economics, 70, 205. google scholar
  • Hanafy, M. & Ming, R. (2021). Machine Learning Approaches for Auto Insurance Big Data. Risks, 9(2), 42. google scholar
  • Hastie, T., Tibshirani, R., Friedman, J. H., & Friedman, J. H. (2009). The elements of statistical learning: data mining, inference, and prediction (Vol. 2, pp. 1-758). New York: springer. google scholar
  • Hu, S., Murphy, T.B. & O’Hagan, A. (2019). Bivariate Gamma Mixture of Experts Models for Joint Insurance Claims Modelling. Cornell University, arXiv: arxiv.org/abs/1904.04699. google scholar
  • Hu, S., Murphy, T.B. & O’Hagan, A. (2021). MvClaim: An R Package for Multivariate General Insurance Claims Severity Modelling. Annals of Actuarial Science, 15(2), 441-457. google scholar
  • Jeong, H., Valdez, E. A., Ahn, J. Y. & Park, S. (2017). Generalized Linear Mixed Models for Dependent Compound Risk Models. SSRN 3045360. google scholar
  • Klugman, S.A., Panjer, H.H. & Willmot, G.E. (2012). Loss models: from data to decisions. John Wiley & Sons, 715. google scholar
  • Kramer, N., Brechmann, E.C., Silvestrini, D. & Czado, C. (2013). Total Loss Estimation Using Copula-Based Regression Models. Insurance: Mathematics and Economics, 53, 829. google scholar
  • Masarotto, G. & Varin, C. (2017). Gaussian Copula Regression in R. Journal of Statistical Software, 77 (8). google scholar
  • Murphy, K. P. (2012). Machine learning: a probabilistic perspective. MIT press. google scholar
  • Nelsen, R.B. (2007). An Introduction to Copulas. Springer science & business media. google scholar
  • Parsa R.A. & Klugman, S.A. (2011). Copula Regression. Variance Advancing and Science of Risks, 5, 45. google scholar
  • Purhadi, B. & Purnami, S. (2018). Parameter Estimation and Statistical Test in Bivariate Gamma Regression Model. 8th Annual Basic Science Onternational Conference. google scholar
  • Ren, J. (2012). A Multivariate Aggregate Loss Model. Insurance: Mathematics and Economics, 51, 402. google scholar
  • Singh, R., Ayyar, M.P., Pavan, T.V.S., Gosain, S. & Shah, R.R. (2019). Automating Car Insurance Claims Using Deep Learning Techniques. google scholar
  • IEEE fifth international conference on multimedia big data (BigMM), 199-207. google scholar
  • Sklar, A. (1959). Fonctions de repartition a n dimensions et leurs marges. Publications de l’Institut Statistique de l’Universite de Paris, 8, 229-231. google scholar
  • Song, P.X.K (2007). Correlated Data Analysis: Modeling, Analytics, And Applications. Springer Science & Business Media, Ontario, Canada. google scholar
  • Song, P.X.-K., Li, M. & Yuan, Y. (2009). Joint Regression Analysis of Correlated Data Using Gaussian Copulas. Biometrics, 65(1), 60-68. google scholar
  • Su, J. & Furman, E. (2017). A Form of Multivariate Pareto Distribution with Applications to Financial Risk Measurement. ASTIN Bulletin: The Journal of the IAA, 47(1), 331-357. google scholar
  • Şahin, Ş., Nevruz, E., Karageyik, B. B., & Simsek, G. (2020). Destekten Yoksun Kalma Tazminatı Hesaplama Yöntemleri, Şeçkin Yayıncılık, Türkiye. google scholar
  • Şahin, Ş., Karageyik, B. B., Nevruz, E., & Simsek, G. (2021). Aktüerya Bilirkişiliği-İş Göremezlik Tazminatı Hesaplama Yöntemleri, Şeçkin Yayıncılık, Türkiye. google scholar
  • Tatlidil, H. (1996). Uygulamalı Çok Degiskenli İstatistiksel Analiz. Cem Web Ofset Ltd. Sti, Ankara. google scholar
  • Vernic, R. (2000). A Multivariate Generalization of The Generalized Poisson Distribution. ASTIN Bulletin, 30(1), 57-67. google scholar
  • Vernic, R., Bolance, C. & Alemany, R. (2022). Sarmanov Distribution for Modeling Dependence Between the Frequency and the Average Severity of Insurance Claims. Insurance: Mathematics and Economics, 102, 111-125. google scholar
  • Weerasinghe, K.P.M.L.P. & Wijegunasekara, M.C. (2016). A Comparative Study of Data Mining Algorithms in The Prediction of Auto Insurance Claims. European International Journal of Science and Technology, 5(1), 47-54. google scholar
  • Yolal, H.E. (2019). Karayolları Motorlu Araçlar Zorunlu Mali Sorumluluk (Trafik) Sigortalarında Sigorta Tazminatının Ödenmesinde Kusurun Etkisi. ProQuest Dissertations & Theses Global. google scholar
  • Zadeh, A. H. & Bilodeau, M. (2013). Fitting Bivariate Losses with Phase-Type Distributions. Scandinavian Actuarial Journal, 4, 241. google scholar
  • https://www.tsb.org.tr/tr/istatistikler Access date: 06.04.2023 google scholar
  • https://www.tsb.org.tr/media/attachments/Trafik_Genel_%C5%9Eartlar%C4%B1_06122021__Ekler_Dahil.pdf,Trafik Sigortası Genel Şartları, Access date: 21.08.2023 google scholar
Toplam 42 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Ekonometri (Diğer)
Bölüm ARAŞTIRMA MAKALESI
Yazarlar

Övgücan Karadağ Erdemir 0000-0002-4725-3588

Yayımlanma Tarihi 27 Aralık 2023
Gönderilme Tarihi 26 Temmuz 2023
Yayımlandığı Sayı Yıl 2023 Sayı: 39

Kaynak Göster

APA Karadağ Erdemir, Ö. (2023). A Comparative Perspective on Multivariate Modeling of Insurance Compensation Payments with Regression-Based and Copula-Based Models. EKOIST Journal of Econometrics and Statistics(39), 161-171.
 Kapak Resmi İndir