Araştırma Makalesi
BibTex RIS Kaynak Göster

Yıl 2024, Cilt: 42 Sayı: 1, 1115 - 1127, 27.02.2024

Çiğdem Lazoğlu Murat Büyükyazıcı

Öz

Kaynakça

  • REFERENCES
  • [1] Ferri S, Oliveri A. Technical Bases for LTC Covers Including Mortality and Disability Projections. Proc. 31st Astin Colloq., Porto Cervo, Italy: 2000, p. 295–314.
  • [2] Biessy G. Long-term Care Insurance: A Multi-State Semi-Markov Model to Describe the Dependency Process in Elderly People. Bull Français DActuariat 2015;15:41–73.
  • [3] Beekman J. An alternative premium calculation method for certain long-term care coverages. Actuar Res Clear House 1990;2:179–200.
  • [4] Parker G. Stochastic analysis of the interaction between investment and insurance risks. North Am Actuar J 1997;1:55–71. [CrossRef]
  • [5] Deleglise MP, Hess C, Nouet S. Tarification, Provisionnement et pilotage d’un portefeuille dependance. Bull Français d’actuariat 2009;9:70–108.
  • [6] Gauzere F, Commenges D, Letenneur L, Dartigues J. Maladie et dépendance : description des évolutions par des modèles multi-états. Population (Paris) 1999;54:205–222.
  • [7] Czado C, Rudolph F. Application of Survival Analysis Methods to Long Term Care Insurance. Insur Econ 2002;31:395–413. [CrossRef]
  • [8] Helms F, Czado C, Gshlöbl S. Calculation of LTC premiums based on direct estimates. ASTIN Bull J IAA 2005;35:455–469. [CrossRef]
  • [9] Levantesi S, Menzietti M. Managing longevity and disability risks in life annuities with long term care. Insur Math Econ 2012;50:391–401. [CrossRef]
  • [10] Nakagawa T. Stochastic Processes: with Applications to Reliability Theory. Springer Science & Business Media; 2011. [CrossRef]
  • [11] Grabski F. Semi-Markov Processes: Applications in System Reliability and Maintenance. Amsterdam: Elsevier; 2014. [CrossRef]
  • [12] Box-Steffensmeier JM, Zorn CJ. Duration Models and Proportional Hazards in Political Science. Am J Pol Sci 2001;45:972–988. [CrossRef]
  • [13] Wienke A. Frailty Models in Survival Analysis. Boca Raton, Florida: CRC Press; 2010. [CrossRef]
  • [14] Duchateau L, Janssen P. The Frailty Model. Berlin, Heidelberg, Dordrecht, and New York: Springer Science & Business Media; 2007.
  • [15] Celik E, Yalcin N. Solution of multiplicative homogeneous linear differential equations with constant exponentials. New Trends Math Sci 2018;2:58–67. [CrossRef]
  • [16] Nüfus ve Konut Araştırması. Türkiye İstatistik Kurumu 2013.
  • [17] Türkiye İstatistik Kurumu. Hayat Tabloları, 2013-2015. 2016.
  • [18] Cohen MA, Ph D, Miller J, Ingoldsby A. Becoming Disabled After Age 65: The Expected Lifetime Costs of Independent Living. 2005.
  • [19] Sucu M, v.d. Türkiye Sigortalı ve Anüitant Hayat Tablolarının Oluşturulması ve Projeksiyonları. Ankara: 2017.
  • [20] Lazoğlu Ç. Longevity Risk Pricing in Long Term Care Insurance. Hacettepe University, 2017.

Pricing for longevity risk in long-term care insurance

Yıl 2024, Cilt: 42 Sayı: 1, 1115 - 1127, 27.02.2024

Çiğdem Lazoğlu Murat Büyükyazıcı

Öz

The increase in life expectancy due to improved health conditions in recent years has led to the longevity risk. This situation has caused an increase in the demand for health insurance over time, and the importance of long-term care insurance for older people which is designed to cover the long-term care needs has increased. In this study, longevity risk is investigated for the long-term care insurance with classified degrees of dependency. The long-term care insurance model is constructed by using Monte Carlo Simulation method according to two different scenarios: static structure in which the mortality rate does not change over time and dynamic structure in which the mortality rate changes depending on the increasing future life expectancy. The duration of dependency for long-term care insurance is modeled under the Weibull distribution of the semi-Markov process, which is explained by the Cox proportional hazard model and the frailty model. Probabilities of death and transition from a healthy state to a need of care state (dependent) are used from Turkey and France. Under the dependency structure, premiums for long-term care insurance and the reserve required to be allocated are calculated and the change in premiums with the effect of dependency is examined and it is concluded that the longevity risk caused more liability to the insurer.

Anahtar Kelimeler

Long-Term Care Insurance Monte-Carlo Simulation Method Semi-Markov Process Cox Proportional Hazard Rate Frailty Model

Kaynakça

  • REFERENCES
  • [1] Ferri S, Oliveri A. Technical Bases for LTC Covers Including Mortality and Disability Projections. Proc. 31st Astin Colloq., Porto Cervo, Italy: 2000, p. 295–314.
  • [2] Biessy G. Long-term Care Insurance: A Multi-State Semi-Markov Model to Describe the Dependency Process in Elderly People. Bull Français DActuariat 2015;15:41–73.
  • [3] Beekman J. An alternative premium calculation method for certain long-term care coverages. Actuar Res Clear House 1990;2:179–200.
  • [4] Parker G. Stochastic analysis of the interaction between investment and insurance risks. North Am Actuar J 1997;1:55–71. [CrossRef]
  • [5] Deleglise MP, Hess C, Nouet S. Tarification, Provisionnement et pilotage d’un portefeuille dependance. Bull Français d’actuariat 2009;9:70–108.
  • [6] Gauzere F, Commenges D, Letenneur L, Dartigues J. Maladie et dépendance : description des évolutions par des modèles multi-états. Population (Paris) 1999;54:205–222.
  • [7] Czado C, Rudolph F. Application of Survival Analysis Methods to Long Term Care Insurance. Insur Econ 2002;31:395–413. [CrossRef]
  • [8] Helms F, Czado C, Gshlöbl S. Calculation of LTC premiums based on direct estimates. ASTIN Bull J IAA 2005;35:455–469. [CrossRef]
  • [9] Levantesi S, Menzietti M. Managing longevity and disability risks in life annuities with long term care. Insur Math Econ 2012;50:391–401. [CrossRef]
  • [10] Nakagawa T. Stochastic Processes: with Applications to Reliability Theory. Springer Science & Business Media; 2011. [CrossRef]
  • [11] Grabski F. Semi-Markov Processes: Applications in System Reliability and Maintenance. Amsterdam: Elsevier; 2014. [CrossRef]
  • [12] Box-Steffensmeier JM, Zorn CJ. Duration Models and Proportional Hazards in Political Science. Am J Pol Sci 2001;45:972–988. [CrossRef]
  • [13] Wienke A. Frailty Models in Survival Analysis. Boca Raton, Florida: CRC Press; 2010. [CrossRef]
  • [14] Duchateau L, Janssen P. The Frailty Model. Berlin, Heidelberg, Dordrecht, and New York: Springer Science & Business Media; 2007.
  • [15] Celik E, Yalcin N. Solution of multiplicative homogeneous linear differential equations with constant exponentials. New Trends Math Sci 2018;2:58–67. [CrossRef]
  • [16] Nüfus ve Konut Araştırması. Türkiye İstatistik Kurumu 2013.
  • [17] Türkiye İstatistik Kurumu. Hayat Tabloları, 2013-2015. 2016.
  • [18] Cohen MA, Ph D, Miller J, Ingoldsby A. Becoming Disabled After Age 65: The Expected Lifetime Costs of Independent Living. 2005.
  • [19] Sucu M, v.d. Türkiye Sigortalı ve Anüitant Hayat Tablolarının Oluşturulması ve Projeksiyonları. Ankara: 2017.
  • [20] Lazoğlu Ç. Longevity Risk Pricing in Long Term Care Insurance. Hacettepe University, 2017.
Toplam 21 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Klinik Kimya
Bölüm Research Articles
Yazarlar

Çiğdem Lazoğlu 0000-0001-5997-5687

Murat Büyükyazıcı Bu kişi benim 0000-0002-8622-4659

Yayımlanma Tarihi 27 Şubat 2024
Gönderilme Tarihi 14 Mart 2022
Yayımlandığı Sayı Yıl 2024 Cilt: 42 Sayı: 1

Kaynak Göster

Vancouver Lazoğlu Ç, Büyükyazıcı M. Pricing for longevity risk in long-term care insurance. SIGMA. 2024;42(1):1115-27.

IMPORTANT NOTE: JOURNAL SUBMISSION LINK https://eds.yildiz.edu.tr/sigma/