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Articles

A dynamic bivariate common shock model with cumulative effect and its actuarial application

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Pages 890-906 | Received 15 Aug 2017, Accepted 25 Apr 2018, Published online: 11 May 2018

References

  • Alai, D. H., Landsman, Z. & Sherris, M. (2013). Lifetime dependence modelling using a truncated multivariate gamma distribution. Insurance: Mathematics and Economics 52, 542–549.
  • Aven, T. & Jensen, U. (1999). Stochastic models in reliability. New York : Springer.10.1007/b97596
  • Aven, T. & Jensen, U. (2000). A general minimal repair model. Journal of Applied Probability 37, 187–197.10.1017/S0021900200015333
  • Barlow, R. E. & Proschan, F. (1975). Statistical theory of reliability and life testing: Probability models. New York : Holt, Rinehart and Winston.
  • Bowers, N. L., Gerber, H. U., Hickman, J. C., Jones, D. A. & Nesbitt, C. J. (1997). Actuarial mathematics, 2nd ed. Illinois: The Society of Actuaries.
  • Brindley, E. C. & Thompson, W. A. (1972). Dependence and ageing aspects of multivariate survival. Journal of the American Statistical Association 67, 822–830.10.1080/01621459.1972.10481300
  • Carriere, J. F. (2000). Bivariate survival models for coupled lives. Scandinavian Actuarial Journal 2000, 17–32.10.1080/034612300750066700
  • Cha, J. H. & Finkelstein, M. (2011). On new classes of extreme shock models and some generalizations. Journal of Applied Probability 48, 258–270.10.1239/jap/1300198148
  • Cha, J. H. & Mi, J. (2007). Study of a stochastic failure model in a random environment. Journal of Applied Probability 44, 151–163.10.1239/jap/1175267169
  • Denuit, M. & Cornet, A. (1999). Multilife premium calculation with dependent future lifetimes. Journal of Actuarial Practice 7, 147–171.
  • Denuit, M., Dhaene, J., Goovaerts, M. J. & Kaas, R. (2005). Actuarial theory for dependent risks. New York : Wiley.10.1002/0470016450
  • Denuit, M., Frostig, E. & Levikson, B. (2006). Shifts in interest rate and common shock model for coupled lives. Belgian Actuarial Bulletin 6, 1–4.
  • Dhaene, J. & Goovaerts, M. J. (1996). Dependency of risks and stop-loss order. ASTIN Bulletin 26, 201–212.10.2143/AST.26.2.563219
  • Finkelstein, M. & Cha, J. H. (2013). Stochastic modelling for reliability. Shocks, burn-in and heterogeneous populations. London: Springer.
  • Frees, E. W., Carriere, J. & Valdez, E. (1996). Annuity valuation with dependent mortality. The Journal of Risk and Insurance 63, 229–261.10.2307/253744
  • Gourieroux, C. & Lu, Y. (2015). Love and death: A Freund model with frailty. Insurance: Mathematics and Economics 63, 191–203.
  • Hougaard, P. (2000). Analysis of multivariate survival data. New York : Springer.10.1007/978-1-4612-1304-8
  • Ji, M., Hardy, M. R. & Li, J. S. (2011). Markovian approaches to joint-life mortality. North American Actuarial Journal 15, 357–376.10.1080/10920277.2011.10597625
  • Joe, H. (1997). Multivariate models and dependence concepts. Boca Raton, FL: Chapman & Hall/CRC.10.1201/CHMONSTAAPP
  • Kaluszka, M. & Okolewski, A. (2014). A note on multiple life premiums for dependent lifetimes. Insurance: Mathematics and Economics 57, 25–30.
  • Lee, H. & Cha, J. H. (2014). On construction of general classes of bivariate distributions. Journal of Multivariate Analysis 127, 151–159.10.1016/j.jmva.2014.02.007
  • Lee, H. & Cha, J. H. (2015). Construction of two new general classes of bivariate distributions based on stochastic orders. Journal of Multivariate Analysis 142, 75–85.10.1016/j.jmva.2015.08.003
  • Lehmann, E. L. (1966). Some concepts of dependence. Annals of Mathematical Statistics 37, 1137–1153.10.1214/aoms/1177699260
  • Lemoine, A. J. & Wenocur, M. L. (1985). On failure modeling. Naval Research Logistics Quarterly 32, 497–508.10.1002/(ISSN)1931-9193
  • Lemoine, A. J. & Wenocur, M. L. (1986). A note on shot-noise and reliability modeling. Operations Research 34, 320–323.10.1287/opre.34.2.320
  • Lu, Y. (2017). Broken-heart, common life, heterogeneity: Analyzing the spousal mortality dependence. ASTIN Bulletin: The Journal of the International Actuarial Association 47, 837–874.10.1017/asb.2017.8
  • Luciano, E., Spreeuw, J. & Vigna, E. (2008). Modelling stochastic mortality for dependent lives. Insurance: Mathematics and Economics 43, 234–244.
  • Lund, R., McCormic, W. & Xiao, U. (2004). Limiting properties of Poisson shot noise processes. Journal of Applied Probability 41, 911–918.10.1239/jap/1091543433
  • Marshall, A. W. & Olkin, I. (1967). A multivariate exponential distribution. Journal of the American Statistical Association 62, 30–44.10.1080/01621459.1967.10482885
  • Nelsen, R. B. (2006). An introduction to copulas, 2nd ed. New York : Springer.
  • Norberg, R. (1989). Actuarial analysis of dependent lives. Mitteilungen der Schweizerisher Vereinigung der Versicherungsmathematiker 1989, 243–254.
  • Panjer, H. H. (1994). Second to die with possibility of simultaneously death. Product Development News 36, 10–11.
  • Rice, J. (1977). On generalized shot noise. Advances in Applied Probability 9, 553–565.10.2307/1426114
  • Ross, S. M. (1996). Stochastic processes. New York : John Wiley.
  • Shaked, M. & Shanthikumar, J. G. (2007). Stochastic orders. New York : Springer.10.1007/978-0-387-34675-5
  • Spreeuw, J. & Owadally, I. (2013). Investigating the broken-heart effect: A model for short-term dependence between the remaining lifetimes of joint lives. Annals of Actuarial Science 7, 236–257.10.1017/S1748499512000292
  • Wolthuis, H. (2003). Life insurance mathematics (The Markovian model), 2nd ed. Amsterdam: IAE, Universiteit van Amsterdam.
  • Youn, H. & Shemyakin, A. (1999). Statistical aspects of joint life insurance pricing. In 1999 Proceedings of the Business and Statistics Section of the American Statistical Association, pp. 34–38. Baltimore, MD.
  • Youn, H. & Shemyakin, A. (2001). Pricing practices for joint last survivor insurance. Actuarial Research Clearing House 2001, 1.

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