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Dabrowska tahmin yöntemiyle çoklu hayat ürünlerinin fiyatlandırılması

Yıl 2023, Cilt: 16 Sayı: 1, 26 - 38, 29.06.2023

Öz

Bu çalışmada Kaplan-Meier yöntemi kullanılarak, çoklu hayat ürünlerine ilişkin fiyatlandırma yapılmıştır. Bu amaçla, Kanada sigorta verilerinden yararlanılarak ortak yaşamların ölümlülük yapısı incelenmiştir. Bireylerin gelecek yaşam sürelerinin bağımlı ve bağımsız olduğu varsayımı altında, annüite ve sigorta ürünlerinin net tek primleri ile bireylerin bağımlılık durumuna göre net yıllık prim tutarları elde edilmiştir. Sonuç olarak, bağımlılığın sigorta ürünleri üzerindeki etkisi gösterilmiştir.

Kaynakça

  • [1] L. Xiaoming, 2008, Stochastic mortality modelling, PhD Thesis, Department of Statistics University of Toronto, Ontario.
  • [2] N. L. Bowers, H. U. Gerber, J. C. Hickman, D. A. Jones and C. J. Nesbitt, 1997, Actuarial Mathematics, The Society of Actuaries, New York.
  • [3] K. Henshaw, C. Constantinescu and, O. Menoukeu Pamen, 2020, Stochastic Mortality Modelling for Dependent Coupled Lives, Risks, 8(1), 17.
  • [4] N. Ragnar, 1989, Actuarial Analysis of Dependent Lives, Bulletin of the Swiss Association of Actuaries, 2, 243–254.
  • [5] J. Spreeuw, 2006, Types of Dependence and Time-dependent Association Between Two Lifetimes in Single Parameter Copula Models. Scandinavian Actuarial Journal, (5), 286–309.
  • [6] C. M. Parkes, B. Benjamin and R. G. Fitzgerald, 1969, Broken Heart: A Statistical Study of Increased Mortality Among Widowers, British Medical Journal, 1(5646), 740-743.
  • [7] A. Ward, 1976, Mortality of Bereavement, British Medical Journal, 1(6011), 700-702.
  • [8] C. Jagger and C. J. Sutton, 1991, Death After Marital Bereavement-is the Risk Increased?, Statistics in Medicine, 10(3), 395-404.
  • [9] P. Hougaard, B. Harvald and N. V. Holm, 1992, Measuring the Similarities Between the Lifetimes of Adult Danish Twins Born Between 1881–1930, Journal of the American Statistical Association, 87(417), 17-24.
  • [10] A. Sklar, 1959, Fonctions de repartition a n dimensions et leurs marges, Public Instution of Statistical University, 8, 229-231. [11] E. W. Frees, J. F. Carriere and E. Valdez, 1996, Annuity Valuation with Dependent Mortality, The Journal of Risk and Insurance, 63(2), 229-261.
  • [12] E. Kızılok Kara, 2021, On Actuarial Premiums for Joint Last Survivor Life Insurance Based On Asymmetric Dependent Lifetimes. Current Academic Studies in Science and Mathematics Sciences-II, D. E. Yıldız, E. Y. Özkan (Eds), Livre de Lyon, France 33.
  • [13] E. Kızılok Kara, 2022, On the Impact of Asymmetric Dependence in the Actuarial Pricing of Joint Life Insurance Policies, Sains Malaysiana, 51(11), 3807-3817.
  • [14] Ö. Bakar, M. Büyükyazıcı, 2022, Stochastic Analysis of Longevity Risk in Dependent Multiple Life Annuities, Sigma Journal of Engineering and Natural Sciences, 40(2), 235-242.
  • [15], Ö. Karadağ Erdemir, M. Sucu, 2020, Eliptik sözde-kopulalar ile esnek bağımlılık modellemesi, İstatistikçiler Dergisi: İstatistik ve Aktüerya, 13(2), 61-77.
  • [16] Y. Zhang and P. Brockett, 2020, Modeling Stochastic Mortality for Joint Lives Through Subordinators, Insurance: Mathematics and Economics, 95, 166-172.
  • [17] P. Jevti´c and T. R. Hurd, 2017, The Joint Mortality of Couples in Continuous Time, Insurance: Mathematics and Economics, 75, 90–97.
  • [18] O. Walter, W. Patrick, 2021, Ottieno J. and Carolyne O., Positive Stable Frailty Approach in the Construction of Dependence Life-Tables, Open Journal of Statistics, 11(4), 506–523.
  • [19] E. Luciano, E. Vigna, 2005, Non Mean Reverting Affine Processes for Stochastic Mortality, ICER working paper and Proceedings of the XVth International AFIR Colloquium, Zurich.
  • [20] E. Luciano, J. Spreeuw, & E. Vigna, 2008, Modeling Stochastic Mortality for Dependent Lives, Insurance: Mathematics and Economics, 43(2), 234–244.
  • [21] E. L. Kaplan and P. Meier, 1958, Nonparametric Estimation from Incomplete Observations, Journal of the American Statistical Association, 53(282), 457-481.
  • [22] E. T. Lee and, J. Wang, 2003, Statistical Methods for Survival Data Analysis, Vol. 476, John Wiley & Sons.
  • [23] D. M. Dabrowska, 1988, Kaplan–Meier Estimate on the Plane, The Annals of Statistics, 16(4), 1475–1489.
  • [24] H. U. Gerber, 1997, Life insurance mathematics, Springer, Tokyo.

Pricing of multiple life products by Dabrowska estimation method

Yıl 2023, Cilt: 16 Sayı: 1, 26 - 38, 29.06.2023

Öz

In this study, pricing of multiple life products is performed using the Kaplan-Meier method. For this purpose, the mortality structure of joint lives is analysed using Canadian insurance data. Under the assumption that individuals' future life times are dependent and independent, net single premiums of annuities and insurance products and net annual premiums according to the dependency status of individuals are obtained. are calculated. As a result, the effect of dependency on insurance products is shown.

Kaynakça

  • [1] L. Xiaoming, 2008, Stochastic mortality modelling, PhD Thesis, Department of Statistics University of Toronto, Ontario.
  • [2] N. L. Bowers, H. U. Gerber, J. C. Hickman, D. A. Jones and C. J. Nesbitt, 1997, Actuarial Mathematics, The Society of Actuaries, New York.
  • [3] K. Henshaw, C. Constantinescu and, O. Menoukeu Pamen, 2020, Stochastic Mortality Modelling for Dependent Coupled Lives, Risks, 8(1), 17.
  • [4] N. Ragnar, 1989, Actuarial Analysis of Dependent Lives, Bulletin of the Swiss Association of Actuaries, 2, 243–254.
  • [5] J. Spreeuw, 2006, Types of Dependence and Time-dependent Association Between Two Lifetimes in Single Parameter Copula Models. Scandinavian Actuarial Journal, (5), 286–309.
  • [6] C. M. Parkes, B. Benjamin and R. G. Fitzgerald, 1969, Broken Heart: A Statistical Study of Increased Mortality Among Widowers, British Medical Journal, 1(5646), 740-743.
  • [7] A. Ward, 1976, Mortality of Bereavement, British Medical Journal, 1(6011), 700-702.
  • [8] C. Jagger and C. J. Sutton, 1991, Death After Marital Bereavement-is the Risk Increased?, Statistics in Medicine, 10(3), 395-404.
  • [9] P. Hougaard, B. Harvald and N. V. Holm, 1992, Measuring the Similarities Between the Lifetimes of Adult Danish Twins Born Between 1881–1930, Journal of the American Statistical Association, 87(417), 17-24.
  • [10] A. Sklar, 1959, Fonctions de repartition a n dimensions et leurs marges, Public Instution of Statistical University, 8, 229-231. [11] E. W. Frees, J. F. Carriere and E. Valdez, 1996, Annuity Valuation with Dependent Mortality, The Journal of Risk and Insurance, 63(2), 229-261.
  • [12] E. Kızılok Kara, 2021, On Actuarial Premiums for Joint Last Survivor Life Insurance Based On Asymmetric Dependent Lifetimes. Current Academic Studies in Science and Mathematics Sciences-II, D. E. Yıldız, E. Y. Özkan (Eds), Livre de Lyon, France 33.
  • [13] E. Kızılok Kara, 2022, On the Impact of Asymmetric Dependence in the Actuarial Pricing of Joint Life Insurance Policies, Sains Malaysiana, 51(11), 3807-3817.
  • [14] Ö. Bakar, M. Büyükyazıcı, 2022, Stochastic Analysis of Longevity Risk in Dependent Multiple Life Annuities, Sigma Journal of Engineering and Natural Sciences, 40(2), 235-242.
  • [15], Ö. Karadağ Erdemir, M. Sucu, 2020, Eliptik sözde-kopulalar ile esnek bağımlılık modellemesi, İstatistikçiler Dergisi: İstatistik ve Aktüerya, 13(2), 61-77.
  • [16] Y. Zhang and P. Brockett, 2020, Modeling Stochastic Mortality for Joint Lives Through Subordinators, Insurance: Mathematics and Economics, 95, 166-172.
  • [17] P. Jevti´c and T. R. Hurd, 2017, The Joint Mortality of Couples in Continuous Time, Insurance: Mathematics and Economics, 75, 90–97.
  • [18] O. Walter, W. Patrick, 2021, Ottieno J. and Carolyne O., Positive Stable Frailty Approach in the Construction of Dependence Life-Tables, Open Journal of Statistics, 11(4), 506–523.
  • [19] E. Luciano, E. Vigna, 2005, Non Mean Reverting Affine Processes for Stochastic Mortality, ICER working paper and Proceedings of the XVth International AFIR Colloquium, Zurich.
  • [20] E. Luciano, J. Spreeuw, & E. Vigna, 2008, Modeling Stochastic Mortality for Dependent Lives, Insurance: Mathematics and Economics, 43(2), 234–244.
  • [21] E. L. Kaplan and P. Meier, 1958, Nonparametric Estimation from Incomplete Observations, Journal of the American Statistical Association, 53(282), 457-481.
  • [22] E. T. Lee and, J. Wang, 2003, Statistical Methods for Survival Data Analysis, Vol. 476, John Wiley & Sons.
  • [23] D. M. Dabrowska, 1988, Kaplan–Meier Estimate on the Plane, The Annals of Statistics, 16(4), 1475–1489.
  • [24] H. U. Gerber, 1997, Life insurance mathematics, Springer, Tokyo.
Toplam 23 adet kaynakça vardır.

Ayrıntılar

Birincil Dil Türkçe
Konular Risk Analizi
Bölüm Makaleler
Yazarlar

Tuğba Aktaş 0000-0002-2050-8763

Emel Kızılok Kara 0000-0001-7580-5709

Meral Sucu 0000-0002-7991-1792

Erken Görünüm Tarihi 27 Haziran 2023
Yayımlanma Tarihi 29 Haziran 2023
Yayımlandığı Sayı Yıl 2023 Cilt: 16 Sayı: 1

Kaynak Göster

IEEE T. Aktaş, E. Kızılok Kara, ve M. Sucu, “Dabrowska tahmin yöntemiyle çoklu hayat ürünlerinin fiyatlandırılması”, JSSA, c. 16, sy. 1, ss. 26–38, 2023.