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Measuring Long-Term Insurance Contract Biometric Risks

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Actuarial Aspects of Long Term Care

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Abstract

Long Term Care insurance contracts are complex insurance products covering an individual for which pricing and reserving issues are traditionally addressed by the introduction of multi-state models. This type of model allows one to describe the transitions of each insured through different states that correspond to events determining, under the terms of the contract, the respective commitments of the parties. The description of insurance contracts through multi-state models is the subject of several studies in the actuarial literature (cf. [21, 31] or [14]). To implement this approach to pricing or reserving, actuaries need to establish suitable statistical bases.

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Notes

  1. 1.

    On this point, see Chaps. 1–3 by F. Castaneda and F. Lusson.

  2. 2.

    A comparison is proposed by [27].

  3. 3.

    See also http://www.ressources-actuarielles.net/gtmortalite, which proposes a complete analysis framework for the construction of such tables.

  4. 4.

    See, for instance, [51] for a presentation of these techniques or [9] for a very detailed description.

  5. 5.

    The convexity found at age 90 beyond the fifth year of continuance is likely a consequence of a lack of data and could be reduced.

  6. 6.

    The mortality tables used are accessible on http://www.ressources-actuarielles.net/references.

References

  1. Aalen, O.O., Johansen, S.: An empirical transition matrix for non-homogeneous Markov chains based on censored observations. Scand. J. Stat. 5, 141–150 (1978).

    Google Scholar 

  2. Ahcan, A., Medved, D., Olivieri, A., Pitacco, E.: Forecasting mortality for small populations by mixing mortality data. Insur. Math. Econ. 54, 12–27 (2014). https://doi.org/10.1016/j.insmatheco.2013.10.013

    MathSciNet  Google Scholar 

  3. Andersen, P.K., Keiding, N.: Interpretability and importance of functionals in competing risks and multistate models. Stat. Med. 31(11–12), 1074–1088 (2012). https://doi.org/10.1002/sim.4385

    Article  MathSciNet  Google Scholar 

  4. Andersen, P.K., Perme, M.P.: Inference for outcome probabilities in multi-state Models. Lifetime Data Anal. 14(4), 405–431 (2008). https://doi.org/10.1007/s10985-008-9097-x

    Article  MathSciNet  Google Scholar 

  5. Andersen, P.K., Borgan, Ø., Gill, R.D., Keiding N.: Statistical Models Based on Counting Processes, p. 767. Springer, New York Inc., (Springer Series in Statistics) (1993). ISBN: 0–378-97872-0, https://doi.org/10.1002/sim.4780131711

    Article  Google Scholar 

  6. Barrieu, P., Bensusan, H., El Karoui, N., et al.: Understanding, modelling and managing longevity risk: key issues and main challenges. Scand. Actuar. J. 2012, 203–231 (2012). https://doi.org/10.1080/03461238.2010.511034

    Article  MathSciNet  Google Scholar 

  7. Biessy, G.: Continuous-time semi-markov inference of biometric laws associated with a long-term care insurance portfolio. ASTIN Bull. J. IAA 47(2), 527–561 (2017). https://doi.org/10.1017/asb.2016.41

    Article  MathSciNet  Google Scholar 

  8. Biessy G.: A semi-Markov model with pathologies for Long-Term Care Insurance, Working paper (2016). https://doi.org/10.1080/10920277.2014.978025

    Article  MathSciNet  Google Scholar 

  9. Boor, De: A Practical Guide to Splines. Springer-Verlag, Berlin (1978)

    Book  Google Scholar 

  10. Booth, H., Tickle, L.: Mortality modelling and forecasting: a review of methods. Ann. Actuar. Sci. 3, 3–43 (2008). https://doi.org/10.1017/S1748499500000440

    Article  Google Scholar 

  11. Brass, W. (ed.): On the Scale of Mortality, Biological aspects of demography, pp. 69–110 (1972). London, Taylor and Francis

    Google Scholar 

  12. CMIR12.: The Analysis of Permanent Health Insurance Data, Continuous Mortality Investigation Bureau, The Institute of Actuaries and the Faculty of Actuaries (1991)

    Google Scholar 

  13. Charpentier, A. (ed.): Computational Actuarial Science, with R. Chapman and Hall, The R Series (2014)

    MATH  Google Scholar 

  14. Christiansen, M.C.: Multistate models in health insurance. Adv. Stat. Anal. 96, 155–186 (2012). https://doi.org/10.1007/s10182-012-0189-2

    Article  MathSciNet  Google Scholar 

  15. Cox, D.R.: Regression models and life-tables. J. R. Stat. Soc. Ser. B (Methodological) 34, 187–220 (1972). https://doi.org/10.1007/978-1-4612-4380-9_37

    Google Scholar 

  16. Croix J.C., Planchet F., Thérond P.E.: Mortality: a statistical approach to detect model misspecification. Bull. Français d’Actuariat 15(29), 115–130 (2015)

    Google Scholar 

  17. Czado, C., Rudolph, F.: Application of survival analysis methods to long-term care insurance. Insur. Math. Econ. 31(3), 395–413 (2002). https://doi.org/10.1016/S0167-6687(02)00186-5

    MathSciNet  MATH  Google Scholar 

  18. D’Amico, G., Guillen, M., Manca, R.: Full backward non-homogeneous semi-Markov processes for disability insurance models: A Catalunya real data application. Insur. Math. Econ. 45(2) 173–179 (2009). https://doi.org/10.1016/j.insmatheco.2009.05.010

    MathSciNet  MATH  Google Scholar 

  19. Dartigues, J.-F., Gagnon, M., Barberger-Gateau, P., Letenneur, L., Commenges, D., Sauvel, C., Michel, P., Salamon, R.: The PAQUID epidemiological program on brain ageing. Neuroepidemiology 11, 14–18 (1992). https://doi.org/10.1159/000110955

    Article  Google Scholar 

  20. Deléglise, M.P., Hess, C., Nouet, S.: Tarification, provisionnement et pilotage d’un portefeuille Dépendance. Bull. Français d’Actuariat 9(17), 70–108 (2009)

    Google Scholar 

  21. Denuit, M., Robert, C.: Actuariat des assurances de Personnes—Modélisation, tarification et provisionnement, Paris: Economica, p. 405 (Assurance Audit Actuariat) (2007). ISBN: 978-2-7178-5329-2

    Google Scholar 

  22. de Uña-Álvarez, J., Meira-Machado, L.: Nonparametric estimation of transition probabilities in the non-Markov illness-death model: a comparative study. Biometrics 71(2), 364–75 (2015). https://doi.org/10.1111/biom.12288

    Article  MathSciNet  Google Scholar 

  23. Ferri, S., Olivieri, A.: Technical bases for LTC covers including mortality and disability projections. In: Proceedings of the 31th International ASTIN Colloquium, Porto Cervo, pp. 135–155 (2000)

    Google Scholar 

  24. Fong, J.H., Shao, A.W., Sherris, M.: Multistate Actuarial models of functional disability. North Am. Actuar. J. 19, 41–59 (2015). https://doi.org/10.1080/10920277.2014.978025

    Article  MathSciNet  Google Scholar 

  25. Fuino M., Wagner J.: Long-term care models and dependence probability tables by acuity level: new empirical evidence from Switzerland. Insur. Math. Econ. 81, 51–70 (2018). https://doi.org/10.1016/j.insmatheco.2018.05.002

    MathSciNet  MATH  Google Scholar 

  26. Gooley, T.A., Leisenring, W., Crowley, J., Storer, B.E.: Estimation of failure probabilities in the presence of competing risks: new representations of old estimators. Stat. Med. 18(6), 695–706 (1999)

    Article  Google Scholar 

  27. Guibert, Q., Planchet, F.: Construction de lois d’expérience en présence d’évènements concurrents: Application à l’estimation des lois d’incidence d’un contrat dépendance. Bul. Français d’Actuariat 14(27), 5–28 (2014)

    Google Scholar 

  28. Guibert, Q., Planchet, F.: Utilisation des estimateurs de Kaplan-Meier par génération et de Hoem pour la construction de tables de mortalité prospectives. Bull. Français d’Actuariat 17(33), 5–24 (2017)

    Google Scholar 

  29. Guibert, Q., Planchet, F.: Non-parametric inference of transition probabilities based on Aalen-Johansen integral estimators for acyclic multi-state models: Application to LTC insurance. Math. Econ. 82, 21–36 (2018). https://doi.org/10.1016/j.insmatheco.2018.05.004

    MathSciNet  MATH  Google Scholar 

  30. Guibert Q.: Sur l’utilisation des modèles multi-états pour la mesure et la gestion des risques d’un contrat d’assurance, Ph.D. thesis, Université Lyon 1 (2015)

    Google Scholar 

  31. Haberman, S., Pitacco, E.: Actuarial Models for Disability Insurance 1re édn, p. 280. Chapman and Hall/CRC (1998). ISBN: 0-8493-0389-3

    Google Scholar 

  32. Helwich, M.: Duration effects and non-smooth semi-Markov models in life insurance, Ph.D. thesis, University of Rostock (2008)

    Google Scholar 

  33. Hoem, J.M.: Inhomogeneous semi-Markov processes, select actuarial tables, and duration-dependence in demography, Population Dynamics, 251–296 (1972). https://doi.org/10.1016/B978-1-4832-2868-6.50013-8

    Chapter  Google Scholar 

  34. Hoem J.M.: Markov chain models in life insurance. Blätter der DGVFM. 9(2), 91–107 (1969)

    Article  MathSciNet  Google Scholar 

  35. Hougaard, P.: Frailty models for survival data. Lifetime Data Anal. 1(3), 255–273 (1995)

    Article  MathSciNet  Google Scholar 

  36. Janssen, J., de Dominicis, R.: Finite non-homogeneous semi-Markov processes: theoretical and computational aspects. Insur. Math. Econ. 3(3), 157–165 (1984). https://doi.org/10.1016/0167-6687(84)90057-X

    MathSciNet  MATH  Google Scholar 

  37. Janssen, J., et Manca, R.: Applied Semi-Markov Processes. Springer (2006)

    Google Scholar 

  38. Kamega A., Planchet F.: Construction de tables de mortalité prospectives sur un groupe restreint: mesure du risque d’estimation. Bull. Français d’Actuariat 13(25), 5–33 (2013)

    Google Scholar 

  39. Kaplan, E.L., Meier, P.: Nonparametric Estimation from Incomplete Observations. J. Am. Stat. Assoc. 53(282), 457–481 (1958). https://doi.org/10.1080/01621459.1958.10501452

    Article  MathSciNet  Google Scholar 

  40. Keiding, N.: Statistical inference in the Lexis diagram. Philos. Trans. R. Soc. Lond. A: Math. Phys. Eng. Sci. 332, 487–509 (1990). https://doi.org/10.1098/rsta.1990.0128

  41. Klein J.P., Moeschberger M. L. (2003) Survival Analysis, Springer, 560 p., ISBN: 0-387-95399-X

    Google Scholar 

  42. Lee, R.D., Carter, L.R.: Modeling and forecasting U.S. mortality. J. Am. Stat. Assoc. 87, 659–671 (1992). https://doi.org/10.2307/2290201

    MATH  Google Scholar 

  43. Levantesi, S., Menzietti, M.: Managing longevity and disability risks in life annuities with long term care. Insur. Math. Econ. 50, 391–401 (2012). https://doi.org/10.1016/j.insmatheco.2012.01.004

    MathSciNet  MATH  Google Scholar 

  44. Martinussen, T., Scheike, T.H.: Dynamic Regression Models for Survival Data. Springer, Statistics for Biology and Health (2006). https://doi.org/10.1198/jasa.2007.s230

    Article  Google Scholar 

  45. Mathieu, E., Foucher, Y., Dellamonica, P., Daures, J.P.: Parametric and Non-Homogeneous Semi-Markov Process for HIV Control. Methodol. Comput. Appl. Probab. 9(3), 389–397 (2007). https://doi.org/10.1007/s11009-007-9033-7

    Article  MathSciNet  Google Scholar 

  46. Meira-Machado, L., de Uña-Álvarez, J., Cadarso-Suárez, C.: Nonparametric estimation of transition probabilities in a non-Markov illness–death model. Lifetime Data Anal. 12(3), 325–344 (2006)

    Article  MathSciNet  Google Scholar 

  47. Olivieri, A., Pitacco, E.: Facing LTC risks. In: Proceedings of the 32th International ASTIN Colloquium, Washington (2001)

    Google Scholar 

  48. Pitacco, E.: Mortality of disabled people. Technical Report (2012). Available at SSRN: http://ssrn.com/abstract=1992319

  49. Planchet, F., Tomas, J.: Constructing Entity Specific Mortality Table: Adjustment to a Reference. Eur. Actuar. J. 4(2), 247–279 (2014). https://doi.org/10.1007/s13385-014-0095-y

    Article  MathSciNet  MATH  Google Scholar 

  50. Planchet, F., Tomas J.: Uncertainty on Survival Probabilities and Solvency Capital Requirement: Application to LTC Insurance. Scand. Actuar. J. (2014) https://doi.org/10.1080/03461238.2014.925496

    Article  MathSciNet  Google Scholar 

  51. Planchet F., Thérond P. E. (2011) Modélisation statistique des phénomènes de durée—Applications actuarielles, Paris: Economica, (Assurance Audit Actuariat), ISBN: 2-7178-5234-4

    Google Scholar 

  52. Planchet F., Tomas J.: Multidimensional smoothing by adaptive local kernel-weighted log-likelihood with application to long-term care insurance. Insur. Math. Econ. 52, 573–589 (2013). http://dx.doi.org/10.1016/j.insmatheco.2013.03.009

  53. Pritchard, D.J.: Modeling disability in long-term care insurance. North Am. Actuar. J. 10, 48–75 (2006). https://doi.org/10.1080/10920277.2006.10597413

    Article  MathSciNet  Google Scholar 

  54. Putter H., Spitoni C.: Non-parametric estimation of transition probabilities in non-Markov multi-state models: The landmark Aalen–Johansen estimator. Stat. Methods Med. Res. 27(7), 2081–2092 (2016). https://doi.org/10.1177/0962280216674497

    Article  MathSciNet  Google Scholar 

  55. R Development Core Team, R: A Language and Environment for Statistical Computing. Vienna, Austria, (R Foundation for Statistical Computing) (2017). ISBN: 3-900051-07-0

    Google Scholar 

  56. Renshaw, A.E., Haberman. S.: On the graduations associated with a multiple state model for permanent health insurance. Insur. Math. Econ. 17(1), 1–17 (1995)

    MATH  Google Scholar 

  57. Rickayzen, B.D., Walsh, D.E.P.: A Multi-State Model of Disability for the United Kingdom: Implications for Future Need for Long-Term Care for the Elderly. Br. Actuar. J. 8(2), 341–393 (2002)

    Article  Google Scholar 

  58. Titman, A.C.: Transition Probability Estimates for Non-Markov Multi-State Models. Biometrics 71(4), 1034–1041 (2015)

    Article  MathSciNet  Google Scholar 

  59. Tsiatis, A.: A non-identifiability aspect of the problem of competing risks. Proc. Natl. Acad. Sci. 72(1), 20–22 (1975)

    Article  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. CEREMADE, UMR 7534, Université Paris-Dauphine, PSL Research University, 75016, Paris, France

    Quentin Guibert

  2. Univ Lyon - Université Claude Bernard Lyon 1, ISFA, Laboratoire SAF EA2429, 69366, Lyon, France

    Quentin Guibert & Frédéric Planchet

  3. Prim’Act, 42 avenue de la Grande Armée, 75017, Paris, France

    Quentin Guibert & Frédéric Planchet

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  1. Quentin Guibert
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  2. Frédéric Planchet
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Correspondence to Quentin Guibert .

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Editors and Affiliations

  1. Bellows Falls, VT, USA

    Etienne Dupourqué

  2. ISFA, Université Lyon, Lyon, France

    Frédéric Planchet

  3. ISUP, New York, NY, USA

    Néfissa Sator

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Guibert, Q., Planchet, F. (2019). Measuring Long-Term Insurance Contract Biometric Risks. In: Dupourqué , E., Planchet, F., Sator, N. (eds) Actuarial Aspects of Long Term Care. Springer Actuarial. Springer, Cham. https://doi.org/10.1007/978-3-030-05660-5_4

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