IDEAS home Printed from https://ideas.repec.org/a/eee/insuma/v41y2007i3p339-361.html
   My bibliography  Save this article

Modelling the joint distribution of competing risks survival times using copula functions

Author

Listed:
  • Kaishev, Vladimir K.
  • Dimitrova, Dimitrina S.
  • Haberman, Steven

Abstract

The problem of modelling the joint distribution of survival times in a competing risks model, using copula functions, is considered. In order to evaluate this joint distribution and the related overall survival function, a system of non-linear differential equations is solved, which relates the crude and net survival functions of the modelled competing risks, through the copula. A similar approach to modelling dependent multiple decrements was applied by Carriere [Carriere, J., 1994. Dependent decrement theory. Transactions, Society of Actuaries XLVI, 45-65] who used a Gaussian copula applied to an incomplete double-decrement model which makes it difficult to calculate any actuarial functions and draw relevant conclusions. Here, we extend this methodology by studying the effect of complete and partial elimination of up to four competing risks on the overall survival function, the life expectancy and life annuity values. We further investigate how different choices of the copula function affect the resulting joint distribution of survival times and in particular the actuarial functions which are of importance in pricing life insurance and annuity products. For illustrative purposes, we have used a real data set and used extrapolation to prepare a complete multiple-decrement model up to age 120. Extensive numerical results illustrate the sensitivity of the model with respect to the choice of copula and its parameter(s).

Suggested Citation

  • Kaishev, Vladimir K. & Dimitrova, Dimitrina S. & Haberman, Steven, 2007. "Modelling the joint distribution of competing risks survival times using copula functions," Insurance: Mathematics and Economics, Elsevier, vol. 41(3), pages 339-361, November.
    • Handle: RePEc:eee:insuma:v:41:y:2007:i:3:p:339-361
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-6687(06)00181-8
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. John Bryant & James J. Dignam, 2004. "Semiparametric Models for Cumulative Incidence Functions," Biometrics, The International Biometric Society, vol. 60(1), pages 182-190, March.
    2. Arthur Renshaw & Steven Haberman, 2003. "Lee–Carter mortality forecasting: a parallel generalized linear modelling approach for England and Wales mortality projections," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 52(1), pages 119-137, January.
    3. Petros Dellaportas & Adrian F. M. Smith & Photis Stavropoulos, 2001. "Bayesian analysis of mortality data," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 164(2), pages 275-291.
    4. Edward Frees & Emiliano Valdez, 1998. "Understanding Relationships Using Copulas," North American Actuarial Journal, Taylor & Francis Journals, vol. 2(1), pages 1-25.
    5. Valdez, Emiliano A., 2001. "Bivariate analysis of survivorship and persistency," Insurance: Mathematics and Economics, Elsevier, vol. 29(3), pages 357-373, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Herbert Hove & Frank Beichelt & Parmod K. Kapur, 2017. "Estimation of the Frank copula model for dependent competing risks in accelerated life testing," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 8(4), pages 673-682, December.
    2. Tie Chen & Songlin Zheng & Jinzhi Feng, 2017. "Statistical dependency analysis of multiple competing failure causes of fuel cell engines," Journal of Risk and Reliability, , vol. 231(2), pages 83-90, April.
    3. Graziani, Rebecca & NIGRI, ANDREA, 2023. "An Age–Period–Cohort Model in a Dirichlet Framework: A Coherent Causes of Death Estimation," SocArXiv 856yw, Center for Open Science.
    4. Quanrui Song & Jianxu Liu & Songsak Sriboonchitta, 2019. "Risk Measurement of Stock Markets in BRICS, G7, and G20: Vine Copulas versus Factor Copulas," Mathematics, MDPI, vol. 7(3), pages 1-16, March.
    5. N. Unnikrishnan Nair & P. G. Sankaran & Preethi John, 2018. "Modelling bivariate lifetime data using copula," METRON, Springer;Sapienza Università di Roma, vol. 76(2), pages 133-153, August.
    6. Li, Han & Li, Hong & Lu, Yang & Panagiotelis, Anastasios, 2019. "A forecast reconciliation approach to cause-of-death mortality modeling," Insurance: Mathematics and Economics, Elsevier, vol. 86(C), pages 122-133.
    7. Yicheng Zhou & Zhenzhou Lu & Yan Shi & Kai Cheng, 2019. "The copula-based method for statistical analysis of step-stress accelerated life test with dependent competing failure modes," Journal of Risk and Reliability, , vol. 233(3), pages 401-418, June.
    8. Ying Jiao & Yahia Salhi & Shihua Wang, 2021. "Dynamic Bivariate Mortality Modelling," Working Papers hal-03244324, HAL.
    9. Dimitrova, Dimitrina S. & Haberman, Steven & Kaishev, Vladimir K., 2013. "Dependent competing risks: Cause elimination and its impact on survival," Insurance: Mathematics and Economics, Elsevier, vol. 53(2), pages 464-477.
    10. Nicholas Bett & Juma Kasozi & Daniel Ruturwa, 2023. "Dependency Modeling Approach of Cause-Related Mortality and Longevity Risks: HIV/AIDS," Risks, MDPI, vol. 11(2), pages 1-18, February.
    11. Romera, Rosario & Molanes, Elisa M., 2008. "Copulas in finance and insurance," DES - Working Papers. Statistics and Econometrics. WS ws086321, Universidad Carlos III de Madrid. Departamento de Estadística.
    12. Ying Jiao & Yahia Salhi & Shihua Wang, 2022. "Dynamic Bivariate Mortality Modelling," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 917-938, June.
    13. Nicholas Bett & Juma Kasozi & Daniel Ruturwa, 2022. "Temporal Clustering of the Causes of Death for Mortality Modelling," Risks, MDPI, vol. 10(5), pages 1-34, May.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Carlo G. Camarda & Ugofilippo Basellini, 2021. "Smoothing, Decomposing and Forecasting Mortality Rates," European Journal of Population, Springer;European Association for Population Studies, vol. 37(3), pages 569-602, July.
    2. Czado, Claudia & Delwarde, Antoine & Denuit, Michel, 2005. "Bayesian Poisson log-bilinear mortality projections," Insurance: Mathematics and Economics, Elsevier, vol. 36(3), pages 260-284, June.
    3. Dimitrova, Dimitrina S. & Haberman, Steven & Kaishev, Vladimir K., 2013. "Dependent competing risks: Cause elimination and its impact on survival," Insurance: Mathematics and Economics, Elsevier, vol. 53(2), pages 464-477.
    4. Fabrizio Durante & Erich Klement & Carlo Sempi & Manuel Úbeda-Flores, 2010. "Measures of non-exchangeability for bivariate random vectors," Statistical Papers, Springer, vol. 51(3), pages 687-699, September.
    5. Furman, Edward & Landsman, Zinoviy, 2010. "Multivariate Tweedie distributions and some related capital-at-risk analyses," Insurance: Mathematics and Economics, Elsevier, vol. 46(2), pages 351-361, April.
    6. Jevtić, P. & Hurd, T.R., 2017. "The joint mortality of couples in continuous time," Insurance: Mathematics and Economics, Elsevier, vol. 75(C), pages 90-97.
    7. Albrecher Hansjörg & Kantor Josef, 2002. "Simulation of ruin probabilities for risk processes of Markovian type," Monte Carlo Methods and Applications, De Gruyter, vol. 8(2), pages 111-128, December.
    8. Dominik Kortschak & Hansjörg Albrecher, 2009. "Asymptotic Results for the Sum of Dependent Non-identically Distributed Random Variables," Methodology and Computing in Applied Probability, Springer, vol. 11(3), pages 279-306, September.
    9. Hoyle, Edward & Mengütürk, Levent Ali, 2013. "Archimedean survival processes," Journal of Multivariate Analysis, Elsevier, vol. 115(C), pages 1-15.
    10. Han, Qinkai & Wang, Tianyang & Chu, Fulei, 2022. "Nonparametric copula modeling of wind speed-wind shear for the assessment of height-dependent wind energy in China," Renewable and Sustainable Energy Reviews, Elsevier, vol. 161(C).
    11. Einmahl, J.H.J. & Krajina, A. & Segers, J., 2011. "An M-Estimator for Tail Dependence in Arbitrary Dimensions," Discussion Paper 2011-013, Tilburg University, Center for Economic Research.
    12. Y. Malevergne & D. Sornette, 2003. "Testing the Gaussian copula hypothesis for financial assets dependences," Quantitative Finance, Taylor & Francis Journals, vol. 3(4), pages 231-250.
    13. Tai-Hsin Huang & Nan-Hung Liu & Subal C. Kumbhakar, 2018. "Joint estimation of the Lerner index and cost efficiency using copula methods," Empirical Economics, Springer, vol. 54(2), pages 799-822, March.
    14. Benoumechiara Nazih & Bousquet Nicolas & Michel Bertrand & Saint-Pierre Philippe, 2020. "Detecting and modeling critical dependence structures between random inputs of computer models," Dependence Modeling, De Gruyter, vol. 8(1), pages 263-297, January.
    15. Mattia Mezzelani & Gloria Polinesi & Francesca Mariani & Maria Cristina Recchioni, 2021. "Longevity-risk-adjusted global age as a measure of well-being," RIEDS - Rivista Italiana di Economia, Demografia e Statistica - The Italian Journal of Economic, Demographic and Statistical Studies, SIEDS Societa' Italiana di Economia Demografia e Statistica, vol. 75(4), pages 28-30, October-D.
    16. D’Amato, Valeria & Haberman, Steven & Piscopo, Gabriella & Russolillo, Maria, 2012. "Modelling dependent data for longevity projections," Insurance: Mathematics and Economics, Elsevier, vol. 51(3), pages 694-701.
    17. Shapiro, Arnold F., 2004. "Fuzzy logic in insurance," Insurance: Mathematics and Economics, Elsevier, vol. 35(2), pages 399-424, October.
    18. Hobæk Haff, Ingrid, 2012. "Comparison of estimators for pair-copula constructions," Journal of Multivariate Analysis, Elsevier, vol. 110(C), pages 91-105.
    19. Hunt, Andrew & Villegas, Andrés M., 2015. "Robustness and convergence in the Lee–Carter model with cohort effects," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 186-202.
    20. Katrien Antonio & Anastasios Bardoutsos & Wilbert Ouburg, 2015. "Bayesian Poisson log-bilinear models for mortality projections with multiple populations," BAFFI CAREFIN Working Papers 1505, BAFFI CAREFIN, Centre for Applied Research on International Markets Banking Finance and Regulation, Universita' Bocconi, Milano, Italy.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:insuma:v:41:y:2007:i:3:p:339-361. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/505554 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.