Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2022, Cilt: 51 Sayı: 1, 288 - 307, 14.02.2022
https://doi.org/10.15672/hujms.889619

Öz

Kaynakça

  • [1] G. Akarsu, Reinsurance pricing using exposure curve of two dependent risks, MSc thesis, Middle East Technical University, 2018.
  • [2] A. Balbás, B. Balbás and A. Heras, Optimal reinsurance with general risk measures, Insurance Math. Econom. 44 (3), 374-384, 2009.
  • [3] S. Bernegger, The Swiss Re exposure curves and the MBBEFD distribution class 1, Astin Bull. 27 (1), 99-111, 1997.
  • [4] P.J. Boland, Statistical methods in general insurance, in: International Conference on Teaching Statistics, ICOTS-7, 1-6, 2006.
  • [5] K. Borch, The optimal reinsurance treaty, Astin Bull. 5 (2), 293-297, 1969.
  • [6] J. Cai, Y. Fang, Z. Li and G.E. Willmot, Optimal reciprocal reinsurance treaties under the joint survival probability and the joint profitable probability, J. Risk Insur. 80 (1), 145-168, 2013.
  • [7] J. Cai, C. Lemieux and F. Liu, Optimal reinsurance from the perspectives of both an insurer and a reinsurer, Astin Bull. 46 (3), 815-849, 2016.
  • [8] J. Cai and K.S. Tan, Optimal retention for a stop-loss reinsurance under the VaR and CTE risk measures, Astin Bull. 37 (1), 93-112, 2007.
  • [9] A. Castañer and M.M. Claramunt Bielsa, Optimal stop-loss reinsurance: a dependence analysis, Hacet. J. Math. Stat. 45 (2), 497-519, 2014.
  • [10] D.S. Dimitrova and V.K. Kaishev, Optimal joint survival reinsurance: An efficient frontier approach, Insurance Math. Econom. 47 (1), 27-35, 2010.
  • [11] L. Gajek and D. Zagrodny, Insurers optimal reinsurance strategies, Insurance Math. Econom. 27 (1), 105-112, 2000.
  • [12] M. Guerra and M.D.L. Centeno, Optimal reinsurance policy: The adjustment coefficient and the expected utility criteria, Insurance Math. Econom. 42 (2), 529-539, 2008.
  • [13] M. Kaluszka, Mean-variance optimal reinsurance arrangements, Scand. Actuar. J. 1, 28-41, 2004.
  • [14] G. Kara, A. Özmen and G.W. Weber, Stability advances in robust portfolio optimization under parallelepiped uncertainty, CEJOR Cent. Eur. J. Oper. Res. 27 (1), 241-261, 2019.
  • [15] T. Mack and M. Fackler, Exposure-rating in liability reinsurance, Blätter der DGVFM 26 (2), 229-238, 2003.
  • [16] S. Salcedo-Sanz, L. Carro-Calvo, M. Claramunt, A. Castañer and M. Mármol, Effectively tackling reinsurance problems by using evolutionary and swarm intelligence algorithms, Risks 2 (2), 132-145, 2014.
  • [17] R.E. Salzmann, Rating by layer of insurance, in: Proceedings of the Casualty Actuarial Society L, 15-26, 1963.
  • [18] Y.K. Tse, Nonlife Actuarial Models: Theory, Methods and Evaluation, Cambridge University Press, 2009.
  • [19] X. Zhou, H. Zhang and Q. Fan, Optimal limited stop-loss reinsurance under VaR, TVaR, and CTE risk measures, Math. Probl. Eng., Doi:10.1155/2015/143739, 2015.

Optimal premium allocation under stop-loss insurance using exposure curves

Yıl 2022, Cilt: 51 Sayı: 1, 288 - 307, 14.02.2022
https://doi.org/10.15672/hujms.889619

Öz

Determining the retention level in the stop-loss insurance risk premium for both insurer and reinsurer is an important factor in pricing. This paper aims to set optimal reinsurance with respect to the joint behavior of the insurer and the reinsurer under stop-loss contracts. The dependence between the costs of insurer and reinsurer is expressed as a function of retention ($d$) and maximum-cap ($m$) levels. Based on the maximum degree of correlation, the optimal levels for $d$ and $m$ are derived under certain claim distributions (Pareto, Gamma and Inverse Gamma). Accordingly, the risk premium and exposure curves for both parties are based on the selected distributions. Quantification of the premium share over derived exposure curves based on the optimized retention and maximum levels and the maximum loss risk is obtained using VaR and CVaR as risk measures.

Kaynakça

  • [1] G. Akarsu, Reinsurance pricing using exposure curve of two dependent risks, MSc thesis, Middle East Technical University, 2018.
  • [2] A. Balbás, B. Balbás and A. Heras, Optimal reinsurance with general risk measures, Insurance Math. Econom. 44 (3), 374-384, 2009.
  • [3] S. Bernegger, The Swiss Re exposure curves and the MBBEFD distribution class 1, Astin Bull. 27 (1), 99-111, 1997.
  • [4] P.J. Boland, Statistical methods in general insurance, in: International Conference on Teaching Statistics, ICOTS-7, 1-6, 2006.
  • [5] K. Borch, The optimal reinsurance treaty, Astin Bull. 5 (2), 293-297, 1969.
  • [6] J. Cai, Y. Fang, Z. Li and G.E. Willmot, Optimal reciprocal reinsurance treaties under the joint survival probability and the joint profitable probability, J. Risk Insur. 80 (1), 145-168, 2013.
  • [7] J. Cai, C. Lemieux and F. Liu, Optimal reinsurance from the perspectives of both an insurer and a reinsurer, Astin Bull. 46 (3), 815-849, 2016.
  • [8] J. Cai and K.S. Tan, Optimal retention for a stop-loss reinsurance under the VaR and CTE risk measures, Astin Bull. 37 (1), 93-112, 2007.
  • [9] A. Castañer and M.M. Claramunt Bielsa, Optimal stop-loss reinsurance: a dependence analysis, Hacet. J. Math. Stat. 45 (2), 497-519, 2014.
  • [10] D.S. Dimitrova and V.K. Kaishev, Optimal joint survival reinsurance: An efficient frontier approach, Insurance Math. Econom. 47 (1), 27-35, 2010.
  • [11] L. Gajek and D. Zagrodny, Insurers optimal reinsurance strategies, Insurance Math. Econom. 27 (1), 105-112, 2000.
  • [12] M. Guerra and M.D.L. Centeno, Optimal reinsurance policy: The adjustment coefficient and the expected utility criteria, Insurance Math. Econom. 42 (2), 529-539, 2008.
  • [13] M. Kaluszka, Mean-variance optimal reinsurance arrangements, Scand. Actuar. J. 1, 28-41, 2004.
  • [14] G. Kara, A. Özmen and G.W. Weber, Stability advances in robust portfolio optimization under parallelepiped uncertainty, CEJOR Cent. Eur. J. Oper. Res. 27 (1), 241-261, 2019.
  • [15] T. Mack and M. Fackler, Exposure-rating in liability reinsurance, Blätter der DGVFM 26 (2), 229-238, 2003.
  • [16] S. Salcedo-Sanz, L. Carro-Calvo, M. Claramunt, A. Castañer and M. Mármol, Effectively tackling reinsurance problems by using evolutionary and swarm intelligence algorithms, Risks 2 (2), 132-145, 2014.
  • [17] R.E. Salzmann, Rating by layer of insurance, in: Proceedings of the Casualty Actuarial Society L, 15-26, 1963.
  • [18] Y.K. Tse, Nonlife Actuarial Models: Theory, Methods and Evaluation, Cambridge University Press, 2009.
  • [19] X. Zhou, H. Zhang and Q. Fan, Optimal limited stop-loss reinsurance under VaR, TVaR, and CTE risk measures, Math. Probl. Eng., Doi:10.1155/2015/143739, 2015.
Toplam 19 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular İstatistik
Bölüm İstatistik
Yazarlar

Özenç Murat Mert 0000-0002-3500-1826

Sevtap Selcuk-kestel 0000-0001-5647-7973

Yayımlanma Tarihi 14 Şubat 2022
Yayımlandığı Sayı Yıl 2022 Cilt: 51 Sayı: 1

Kaynak Göster

APA Mert, Ö. M., & Selcuk-kestel, S. (2022). Optimal premium allocation under stop-loss insurance using exposure curves. Hacettepe Journal of Mathematics and Statistics, 51(1), 288-307. https://doi.org/10.15672/hujms.889619
AMA Mert ÖM, Selcuk-kestel S. Optimal premium allocation under stop-loss insurance using exposure curves. Hacettepe Journal of Mathematics and Statistics. Şubat 2022;51(1):288-307. doi:10.15672/hujms.889619
Chicago Mert, Özenç Murat, ve Sevtap Selcuk-kestel. “Optimal Premium Allocation under Stop-Loss Insurance Using Exposure Curves”. Hacettepe Journal of Mathematics and Statistics 51, sy. 1 (Şubat 2022): 288-307. https://doi.org/10.15672/hujms.889619.
EndNote Mert ÖM, Selcuk-kestel S (01 Şubat 2022) Optimal premium allocation under stop-loss insurance using exposure curves. Hacettepe Journal of Mathematics and Statistics 51 1 288–307.
IEEE Ö. M. Mert ve S. Selcuk-kestel, “Optimal premium allocation under stop-loss insurance using exposure curves”, Hacettepe Journal of Mathematics and Statistics, c. 51, sy. 1, ss. 288–307, 2022, doi: 10.15672/hujms.889619.
ISNAD Mert, Özenç Murat - Selcuk-kestel, Sevtap. “Optimal Premium Allocation under Stop-Loss Insurance Using Exposure Curves”. Hacettepe Journal of Mathematics and Statistics 51/1 (Şubat 2022), 288-307. https://doi.org/10.15672/hujms.889619.
JAMA Mert ÖM, Selcuk-kestel S. Optimal premium allocation under stop-loss insurance using exposure curves. Hacettepe Journal of Mathematics and Statistics. 2022;51:288–307.
MLA Mert, Özenç Murat ve Sevtap Selcuk-kestel. “Optimal Premium Allocation under Stop-Loss Insurance Using Exposure Curves”. Hacettepe Journal of Mathematics and Statistics, c. 51, sy. 1, 2022, ss. 288-07, doi:10.15672/hujms.889619.
Vancouver Mert ÖM, Selcuk-kestel S. Optimal premium allocation under stop-loss insurance using exposure curves. Hacettepe Journal of Mathematics and Statistics. 2022;51(1):288-307.