Longevity Risk and Modelling in The Life and Pension Insurance Company

Abstract

Longevity risk is exactly the opposite of mortality risk and indicates that live longer than life expectancy has a cost for insurance companies. Longevity risk is one of the important topics which take part in actuary literature. One of the most widely used model is Lee-Carter (LC) model which allow to be expressed as a stochastic process of mortality models. The study was carried out in order to model male and female mortality rates in Turkey by means of Lee-Carter (LC) method and in order to make predictions for the future. Thus, male and female death rates associated with age between 1950-2020 years of Turkish statistical institute in Turkey was used as data. At the end of study, it was found that death rate of men may be more than those females for the future.

Keywords

• Insurance
• Longevity Risk
• Mortality Risk

References

1. Antolin, P. (2007). Longevity Risk and Private Pensions, OECD Working Papers on Insurance and Private Pensions, No. 3, OECD Publishing.
2. Arık, A. ve Sucu, M. (2011). Uzun Ömürlülük Bonolarını Fiyatlandırma: Uç Değer Kuramı ve Kübik Risk Fiyatlandırma Modeli, İstatistikçiler Dergisi, 4 (2011) 69-85.
3. Black, K. and H.D. Skipper.(2000). Life & Health Insurance, Prentice Hall, NJ, USA.
4. Booth, H., Maindonald, J. and Smith, L. (2002). Age-Time Interactions in Mortality Projection: Applying Lee-Carter to Australia, ANU, Demography and Sociology Program, Research School of Social Sciences, Working Papers No. 85.
5. Brouhns, N. Denuit, M. and Vermunt, J.K. (2002). A Poisson log-bilinear Regression Approach to the Construction of Projected Lifetables. Insurance: Mathematics and Economics. 31 (2002) 373–393.
6. Brouhns, N., Denuit, M., Vermunt, J. (2002) A Poisson Log-Linear regression approach to the construction of projected life tables, Insurance: Mathematics and Finance, 31, 373-393.
7. Butt Z. Haberman S. (2004). Application of Frailty-Based Mortality Models Using Generalized Linear Models, ASTIN Bulletin, Vol 34, Issue 1, 175-197.
8. Chan, W.S. (2013) Longevity Risk: Recent Developments and Actuarial Implications, The Chinese University of Hong Kong, Master Thesis, A SOA Center of Actuarial Excellence.

9. Coxa, S. H., Y. Lin and H. Pedersen. (2010). Mortality Risk Modeling: Applications to Insurance Securitization, Insurance: Mathematics and Economics, 46, 242-253, journal homepage: www.elsevier.com/locate/ime
10. Currie, L.D. (2013). Smoothing Constrained Generalized Linear Models With an Application to the Lee-Carter Model. Statistical Modelling 2013; 13(1): 69–93.
11. Danesi, L.I., Haberman, S., Millossovich, P. (2015) Forecasting mortality in subpopulations using Lee–Carter type models: A comparison, Insurance: Mathematics and Economics 62 (2015) 151–161.
12. De Jong, P. and Tickle, L. (2006). Extending Lee-Carter Mortality Forecasting, Mathematical Population Studies 13(1), 1–18.
13. Gatzert, N. and Wesker, H. (2012). Mortality Risk and its Effect on Shortfall and Risk Management in Life Insurance, The Journal of Risk and Insurance, Vol. 00, No. 0, 1-34.
14. Gençtürk, Y., Genç, T. (2012). Türkiye İl-İlçe Merkezlerindeki Ölüm Oranlarının Trend ve Lee-Carter Yöntemleri ile Tahmini, Anadolu Unıversıty Journal Of Scıence And Technology. Cilt/Vol.: 2-Sayı/No: 1 : 63-74.
15. Haberman, S. Russolillo, M. (2005). Lee-Carter Mortality Forecasting: Application to the Italian population, City University – Actuarial Research Paper No. 167.
16. Hanewald, K., J. Piggott and M. Sherris. (2013). “Individual Post-retirement Longevity Risk Management under Systematic Mortality Risk”. Insurance: Mathematics and Economics 52, 87–97.
17. Hàri, N. Waegenaere, A.D. Melenberg, B. and Nijman, T.E. (2007). Estimating the Term Structure of Mortality. Insurance: Mathematics and Economics. 42, 492-504.
18. Heale, B. (2013). Stress and Scenario Testing: How Insurers Compare With Banks, Stress Testing: European Edition. Moody’s Analytics. Vol 1, September, p.80-86.
19. Hyndman, R.J. and Ullah, M.S. (2007). Robust Forecasting of Mortality and Fertility Rates: A Functional Data Approach, Computational Statistics and Data Analysis 51(10), 4942–4956.
20. Ilic, M.M., V.Avdalovic and M. D. Obadovic. (2011). Development of Model for Insurance Risk Management and its Application to Insurance Companies Operating in the Serbian Market, Journal of Business Management and Economics, 2(6), 223-228
21. Kogure, A. and Kurachi, Y. (2010). A Bayesian Approach to Pricing Longevity Risk Based on Risk-Neutral Predictive Distributions. Insurance: Mathematics and Economics. 46 (2010) 162-172.
22. Koissi, M.C. and Shapiro, A.F. (2008). The Lee-Carter Model Under The Condition of VariablesAge-Specific Parameters, Actuarial Research Conference, Regina, Canada, 2.
23. Kwon, H.S. and Jones, B. L. (2008). Applications of a Multi-State Risk Factor/mortality Model in Life Insurance, Insurance: Mathematics and Economics, 43, 394-402.
24. Lee, R. and Miller, T. (2001). Evaluating the Performance of Lee-Carter Mortality Forecasts, Demography 38(4), 537-549.
25. Lee, R.D. and Carter, L. (1992). Modeling and Forecasting U.S. Mortality, Journal of the American Statistical Association. 87, 419.
26. Richards, S.J., Currie, I.D. (2009) Longevity Risk and Annuity Pricing With the Lee-Carter Model, British Actuarial Journal, 15, II, 317-365.
27. Richards, S.J., I. D. Currie and G. P. Ritchie. (2012). A Value-at-Risk Framework for Longevity Trend Risk, A Discussion Paper, Presented to the Institute and Faculty of Actuaries, London.
28. Wiśniowski, A., et al., (2015) Bayesian Population Forecasting: Extending the Lee-Carter Method, Demography (2015) 52:1035–1059.
29. Yıldırım, F. (2010) Türkiye Ölümlülük Yapısının Lee-Carter Ve Bulanık Lee-Carter İle Modellenmesi, Yayınlanmamış Yüksek Lisans Tezi, Hacettepe Üniversitesi, Fen Bilimleri Enstitüsü.