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Survival probabilities for compound binomial risk model with discrete phase-type claims

Yıl 2016, Cilt: 65 Sayı: 2, 11 - 22, 01.08.2016
https://doi.org/10.1501/Commua1_0000000755

Öz

Due to having useful properties in approximating to the other
distributions and mathematically tractable, phase type distributions are commonly used in actuarial risk theory. Claim occurrence time and individual
claim size distributions are modelled by phase type distributions in literature.
This paper aims to calculate the survival probabilities of an insurance company under the assumption that compound binomial risk model where the
individual claim sizes are distributed as discrete Phase Type distribution

Kaynakça

  • Asmussen, S., 2000. Ruin probabilities. World Scienti…c, Singapore.
  • Bladt, M. 2005. A review on phase-type distributions and their use in risk theory. Astin Bulletin, 35(01), 145-161.
  • Breuer, L., and Baum, D. 2005. Phase-Type Distributions. An Introduction to Queueing Theory and Matrix-Analytic Methods, 169-184.
  • Chen, X. H., Dempster, A. P., and Liu, J. S. 1994. Weighted …nite population sampling to maximize entropy. Biometrika, 81(3), 457-469.
  • Dickson, D. C. 1994. Some comments on the compound binomial model. Astin Bulletin, 24(01), 33-45.
  • Drekic, S. 2006. Phase-Type Distribution. Encyclopedia of Quantitative Finance.
  • Eryilmaz S., 2014. On distributions of runs in the compound binomial risk model, Methodol. Comput. Appl. Probab. 16 (1).149-159.
  • Gerber, H. U. 1988. Mathematical fun with the compound binomial process. Astin Bulletin, 18(02), 161-168.
  • Latouche, G., Ramaswami, V., 1999. Introduction to matrix analytic methods in stochastic modeling. ASA SIAM, Philadelphia
  • Li, S., and Sendova, K. P. 2013. The …nite-time ruin probability under the compound binomial risk model. European Actuarial Journal, 3(1), 249-271.
  • Liu, G., Wang, Y., and Zhang, B. 2005. Ruin probability in the continuous-time compound binomial model. Insurance: Mathematics and Economics, 36(3), 303-316.
  • Liu, G., and Zhao, J. 2007. Joint distributions of some actuarial random vectors in the compound binomial model. Insurance: Mathematics and Economics, 40(1), 95-103.
  • Neuts, M.F., 1975. Probability distributions of phase type. University of Louvain, pp. 173-206. [14] Neuts, M.F., 1981. Matrix-geometric solutions in stochastic models: An algorithmic ap- proach.Johns Hopkins University Press, Baltimore.
  • Stanford, D.A., Stroinski, K.J., 1994. Recursive methods for computing …nite-time ruin prob- abilities for phase-distributed claim sizes. ASTIN Bull. 24, 235-254.
  • Shiu, E. S. 1989. The probability of eventual ruin in the compound binomial model. Astin Bulletin, 19(2), 179-190.
  • Tank, F., and Tuncel, A. 2015. Some results on the extreme distributions of surplus process with nonhomogeneous claim occurrences. Hacettepe Journual of Mathematics and Statistics 44(2), 475-484.
  • Tank, F., and Eryilmaz, S. 2015. The distributions of sum, minima and maxima of generalized geometric random variables. Statistical Papers 56(4), 1191-1203.
  • Tuncel, A., and Tank, F. 2014. Computational results on the compound binomial risk model with nonhomogeneous claim occurrences. Journal of Computational and Applied Mathemat- ics, 263, 69-77.
  • Willmot, G. E. 1993. Ruin probabilities in the compound binomial model. Insurance: Math- ematics and Economics, 12(2), 133-142.
  • Wu, X. and Li, S., 2008. On a discrete-time Sparre Anderson model with phase-type claims, Working paper 08-169, Department of Economics, 1–16. University of Melbourne, http://www.mercury.ecom.unimelb.edu.au/SITE/actwww/wps2008/No169.pdf.
  • Current address : Altan TUNCEL: Kirikkale University, Faculty of Arts and Sciences, Depart- ment of Actuarial Sciences, Yahsihan- Kirikkale, TURKEY
  • E-mail address : atuncel@kku.edu.tr
Yıl 2016, Cilt: 65 Sayı: 2, 11 - 22, 01.08.2016
https://doi.org/10.1501/Commua1_0000000755

Öz

Kaynakça

  • Asmussen, S., 2000. Ruin probabilities. World Scienti…c, Singapore.
  • Bladt, M. 2005. A review on phase-type distributions and their use in risk theory. Astin Bulletin, 35(01), 145-161.
  • Breuer, L., and Baum, D. 2005. Phase-Type Distributions. An Introduction to Queueing Theory and Matrix-Analytic Methods, 169-184.
  • Chen, X. H., Dempster, A. P., and Liu, J. S. 1994. Weighted …nite population sampling to maximize entropy. Biometrika, 81(3), 457-469.
  • Dickson, D. C. 1994. Some comments on the compound binomial model. Astin Bulletin, 24(01), 33-45.
  • Drekic, S. 2006. Phase-Type Distribution. Encyclopedia of Quantitative Finance.
  • Eryilmaz S., 2014. On distributions of runs in the compound binomial risk model, Methodol. Comput. Appl. Probab. 16 (1).149-159.
  • Gerber, H. U. 1988. Mathematical fun with the compound binomial process. Astin Bulletin, 18(02), 161-168.
  • Latouche, G., Ramaswami, V., 1999. Introduction to matrix analytic methods in stochastic modeling. ASA SIAM, Philadelphia
  • Li, S., and Sendova, K. P. 2013. The …nite-time ruin probability under the compound binomial risk model. European Actuarial Journal, 3(1), 249-271.
  • Liu, G., Wang, Y., and Zhang, B. 2005. Ruin probability in the continuous-time compound binomial model. Insurance: Mathematics and Economics, 36(3), 303-316.
  • Liu, G., and Zhao, J. 2007. Joint distributions of some actuarial random vectors in the compound binomial model. Insurance: Mathematics and Economics, 40(1), 95-103.
  • Neuts, M.F., 1975. Probability distributions of phase type. University of Louvain, pp. 173-206. [14] Neuts, M.F., 1981. Matrix-geometric solutions in stochastic models: An algorithmic ap- proach.Johns Hopkins University Press, Baltimore.
  • Stanford, D.A., Stroinski, K.J., 1994. Recursive methods for computing …nite-time ruin prob- abilities for phase-distributed claim sizes. ASTIN Bull. 24, 235-254.
  • Shiu, E. S. 1989. The probability of eventual ruin in the compound binomial model. Astin Bulletin, 19(2), 179-190.
  • Tank, F., and Tuncel, A. 2015. Some results on the extreme distributions of surplus process with nonhomogeneous claim occurrences. Hacettepe Journual of Mathematics and Statistics 44(2), 475-484.
  • Tank, F., and Eryilmaz, S. 2015. The distributions of sum, minima and maxima of generalized geometric random variables. Statistical Papers 56(4), 1191-1203.
  • Tuncel, A., and Tank, F. 2014. Computational results on the compound binomial risk model with nonhomogeneous claim occurrences. Journal of Computational and Applied Mathemat- ics, 263, 69-77.
  • Willmot, G. E. 1993. Ruin probabilities in the compound binomial model. Insurance: Math- ematics and Economics, 12(2), 133-142.
  • Wu, X. and Li, S., 2008. On a discrete-time Sparre Anderson model with phase-type claims, Working paper 08-169, Department of Economics, 1–16. University of Melbourne, http://www.mercury.ecom.unimelb.edu.au/SITE/actwww/wps2008/No169.pdf.
  • Current address : Altan TUNCEL: Kirikkale University, Faculty of Arts and Sciences, Depart- ment of Actuarial Sciences, Yahsihan- Kirikkale, TURKEY
  • E-mail address : atuncel@kku.edu.tr
Toplam 22 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Research Article
Yazarlar

Altan Tuncel Bu kişi benim

Yayımlanma Tarihi 1 Ağustos 2016
Yayımlandığı Sayı Yıl 2016 Cilt: 65 Sayı: 2

Kaynak Göster

APA Tuncel, A. (2016). Survival probabilities for compound binomial risk model with discrete phase-type claims. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 65(2), 11-22. https://doi.org/10.1501/Commua1_0000000755
AMA Tuncel A. Survival probabilities for compound binomial risk model with discrete phase-type claims. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. Ağustos 2016;65(2):11-22. doi:10.1501/Commua1_0000000755
Chicago Tuncel, Altan. “Survival Probabilities for Compound Binomial Risk Model With Discrete Phase-Type Claims”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 65, sy. 2 (Ağustos 2016): 11-22. https://doi.org/10.1501/Commua1_0000000755.
EndNote Tuncel A (01 Ağustos 2016) Survival probabilities for compound binomial risk model with discrete phase-type claims. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 65 2 11–22.
IEEE A. Tuncel, “Survival probabilities for compound binomial risk model with discrete phase-type claims”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., c. 65, sy. 2, ss. 11–22, 2016, doi: 10.1501/Commua1_0000000755.
ISNAD Tuncel, Altan. “Survival Probabilities for Compound Binomial Risk Model With Discrete Phase-Type Claims”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 65/2 (Ağustos 2016), 11-22. https://doi.org/10.1501/Commua1_0000000755.
JAMA Tuncel A. Survival probabilities for compound binomial risk model with discrete phase-type claims. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2016;65:11–22.
MLA Tuncel, Altan. “Survival Probabilities for Compound Binomial Risk Model With Discrete Phase-Type Claims”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, c. 65, sy. 2, 2016, ss. 11-22, doi:10.1501/Commua1_0000000755.
Vancouver Tuncel A. Survival probabilities for compound binomial risk model with discrete phase-type claims. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2016;65(2):11-22.

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Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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