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RUIN PROBABILITIES IN DEPENDENT INSURANCES WITH AUTOREGRESSIVE MODEL

Year 2018, Volume: 7 Issue: 4, 365 - 375, 30.12.2018
https://doi.org/10.17261/Pressacademia.2018.997

Abstract

Purpose- Risk analysis and ruin probabilities were calculated with the assumption of independence in the past, however this assumption
does not reflect the reality at the present time. Today, insurance activities are more advanced, and consumers are more informed, for this
reason existence of dependency between insurance branches within the portfolio of an insurance firm, is unavoidable. Aim of this study is
to calculate the ruin probability for two dependent insurance branches.
Methodology- In this study, monthly claim data of a leading insurance firm which belongs to two different insurance branches namely
traffic and health, in the period of 2007-2016 are used.
Findings- In the case of fixed interest rate and initial capital, it’s found that if dependence of insurance branches decreases, ruin
probabilities decrease.
Conclusion- In the case of fixed interest rate and initial capital, to decrease the ruin probability, dependence of branches should be
decreased. To lower the dependence, collected premiums should be increased, thus lower adjustment coefficients can be obtained.
Accordingly, with the lower adjustment coefficient, ruin probabilities can be decreased.

References

  • Bayramoğlu, M. M. (2018). Türkiye’de oduna dayalı orman ürünleri üzerine bir araştırma: zaman serisi analizi. Artvin Çoruh Üniversitesi Orman Mühendisliği Dergisi, 1: 18 – 26. DOI: 10.17474/artvinofd.333344
  • Cai, J., Li, H. (2007). Dependence properties and bounds for ruin probabilities in multivariate compound risk models. Journal of Multivariate Analysis, 98: 757-773. DOI: 10.1016/j.jmva.2006.06.004
  • Cossette, H., Marceau, E., Deschamps, W. M. (2010). Discrete-Time risk models based on time series for count random variables. The Journal of International Actuarial Association, 40(1): 123-150. DOI: 10.2143/AST.40.1.2049221
  • Dağlıoğlu, S., Erdemir, C. (2008a). Bazı bağımlı aktüeryal risk süreçlerinin deneysel sonuçları. İstatistikçiler Dergisi, 2: 105 – 124. Retrieved from http://www.istatistikciler.org/dergi/IstDer080204.pdf
  • Dağlıoğlu, S., Erdemir, C. (2008b). Bağımlı aktüeryal risklerin çok değişkenli zaman serisi modeli. İstatistikçiler Dergisi, 1: 144 – 163. Retrieved from http://dergipark.gov.tr/download/article-file/105645
  • Gu, C. (2013). The ruin problem of dependent risk model based on copula function. Journal of Chemical and Pharmaceutical Research, 5(9): 234-240. Retrieved from http://www.jocpr.com/articles/the-ruin-problem-of-dependent-risk-model-based-on-copula-function.pdf
  • Heilpern, S. (2009). Probability of ruin for a dependent, two-dimensional poisson process. Operations Research And Decision, 1: 77 – 90. Retrieved from https://www.researchgate.net/publication/227653942_Probability_of_ruin_for_a_dependent_two-dimensional_poisson_process
  • Jiang, W., Yang, Z. (2016). The maximum surplus before ruin for dependent risk models through farlie–gumbel–morgenstern copula. Scandinavian Actuarial Journal, 2016(5): 385-397. DOI: 10.2139/ssrn.2460490
  • Liosel S. and Lefevre C. (2009). Finite-Time ruin probabilities for discrete, possibly dependent, claim severities. Methodology And Computing In Applied Probability, 11(3): 425-441. DOI: 10.1007/s11009-009-9123-9
  • Makridakis, S., Wheelwright, S. C., Hyndman, R. J. (1998). Forecasting: methods and applications. John Wiley & Sons. Inc, United State of America.
  • Tse, Yiu-Kues (2009). Nonlife actuarial models theory, methods and evaluation. Cambridge Unıversity Press, New York.
  • Wan, L. M., Yuen, K. C., Li, W. K. (2005). Ultimate ruin probability for a time-series risk model with dependent classes of ınsurance business. Journal of Actuarial Practice, 12: 193-214. Retrieved from http://digitalcommons.unl.edu/cgi/viewcontent.cgi?article=1027&context=joap
  • Wang, S., Dhaene, J. (1998). Comonotonicity, correlation order and premium principles. Insurance: Mathematics and Economics, 22: 235 – 242. DOI: 10.1016/S0167-6687(97)00040-1
  • Wu, X. W., Yuen, K. C. (2003). A discrete-time risk model with interaction between classes of business. Insurance: Mathematics and Economics, 33: 117-133. DOI: 10.1016/S0167-6687(03)00148-3
  • Yang, H. (2003). Ruin theory in a financial corporation model with credit risk. Insurance: Mathematics and Economics, 33: 135-145. DOI: 10.1016/S0167-6687(03)00149-5
  • Yang, H., Zhang, L. (2006). Ruin problems for a discrete time risk model with random interest rate. Mathematical Methods of Operations Research, 63(2): 287-299. DOI: 10.1007/s00186-005-0025-5
  • Zhang, Z., Yuen, K. C., Li, W. K. (2007). A Time-Series risk model with constant interest for dependent classes of business. Insurance: Mathematics and Economics, 41: 32-40. DOI: 10.1016/j.insmatheco.2006.08.006
Year 2018, Volume: 7 Issue: 4, 365 - 375, 30.12.2018
https://doi.org/10.17261/Pressacademia.2018.997

Abstract

References

  • Bayramoğlu, M. M. (2018). Türkiye’de oduna dayalı orman ürünleri üzerine bir araştırma: zaman serisi analizi. Artvin Çoruh Üniversitesi Orman Mühendisliği Dergisi, 1: 18 – 26. DOI: 10.17474/artvinofd.333344
  • Cai, J., Li, H. (2007). Dependence properties and bounds for ruin probabilities in multivariate compound risk models. Journal of Multivariate Analysis, 98: 757-773. DOI: 10.1016/j.jmva.2006.06.004
  • Cossette, H., Marceau, E., Deschamps, W. M. (2010). Discrete-Time risk models based on time series for count random variables. The Journal of International Actuarial Association, 40(1): 123-150. DOI: 10.2143/AST.40.1.2049221
  • Dağlıoğlu, S., Erdemir, C. (2008a). Bazı bağımlı aktüeryal risk süreçlerinin deneysel sonuçları. İstatistikçiler Dergisi, 2: 105 – 124. Retrieved from http://www.istatistikciler.org/dergi/IstDer080204.pdf
  • Dağlıoğlu, S., Erdemir, C. (2008b). Bağımlı aktüeryal risklerin çok değişkenli zaman serisi modeli. İstatistikçiler Dergisi, 1: 144 – 163. Retrieved from http://dergipark.gov.tr/download/article-file/105645
  • Gu, C. (2013). The ruin problem of dependent risk model based on copula function. Journal of Chemical and Pharmaceutical Research, 5(9): 234-240. Retrieved from http://www.jocpr.com/articles/the-ruin-problem-of-dependent-risk-model-based-on-copula-function.pdf
  • Heilpern, S. (2009). Probability of ruin for a dependent, two-dimensional poisson process. Operations Research And Decision, 1: 77 – 90. Retrieved from https://www.researchgate.net/publication/227653942_Probability_of_ruin_for_a_dependent_two-dimensional_poisson_process
  • Jiang, W., Yang, Z. (2016). The maximum surplus before ruin for dependent risk models through farlie–gumbel–morgenstern copula. Scandinavian Actuarial Journal, 2016(5): 385-397. DOI: 10.2139/ssrn.2460490
  • Liosel S. and Lefevre C. (2009). Finite-Time ruin probabilities for discrete, possibly dependent, claim severities. Methodology And Computing In Applied Probability, 11(3): 425-441. DOI: 10.1007/s11009-009-9123-9
  • Makridakis, S., Wheelwright, S. C., Hyndman, R. J. (1998). Forecasting: methods and applications. John Wiley & Sons. Inc, United State of America.
  • Tse, Yiu-Kues (2009). Nonlife actuarial models theory, methods and evaluation. Cambridge Unıversity Press, New York.
  • Wan, L. M., Yuen, K. C., Li, W. K. (2005). Ultimate ruin probability for a time-series risk model with dependent classes of ınsurance business. Journal of Actuarial Practice, 12: 193-214. Retrieved from http://digitalcommons.unl.edu/cgi/viewcontent.cgi?article=1027&context=joap
  • Wang, S., Dhaene, J. (1998). Comonotonicity, correlation order and premium principles. Insurance: Mathematics and Economics, 22: 235 – 242. DOI: 10.1016/S0167-6687(97)00040-1
  • Wu, X. W., Yuen, K. C. (2003). A discrete-time risk model with interaction between classes of business. Insurance: Mathematics and Economics, 33: 117-133. DOI: 10.1016/S0167-6687(03)00148-3
  • Yang, H. (2003). Ruin theory in a financial corporation model with credit risk. Insurance: Mathematics and Economics, 33: 135-145. DOI: 10.1016/S0167-6687(03)00149-5
  • Yang, H., Zhang, L. (2006). Ruin problems for a discrete time risk model with random interest rate. Mathematical Methods of Operations Research, 63(2): 287-299. DOI: 10.1007/s00186-005-0025-5
  • Zhang, Z., Yuen, K. C., Li, W. K. (2007). A Time-Series risk model with constant interest for dependent classes of business. Insurance: Mathematics and Economics, 41: 32-40. DOI: 10.1016/j.insmatheco.2006.08.006
There are 17 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Elif Makbule Cekici 0000-0002-1603-9896

Sami Ozcan 0000-0002-7654-7614

Hasan Durmus This is me 0000-0001-8240-4671

Publication Date December 30, 2018
Published in Issue Year 2018 Volume: 7 Issue: 4

Cite

APA Cekici, E. M., Ozcan, S., & Durmus, H. (2018). RUIN PROBABILITIES IN DEPENDENT INSURANCES WITH AUTOREGRESSIVE MODEL. Journal of Business Economics and Finance, 7(4), 365-375. https://doi.org/10.17261/Pressacademia.2018.997

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