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The Impact of Stress Factors on the Price of Widow’s Pensions

Chapter
Part of the EAA Series book series (EAAS)

Abstract

A model of joint life insurance with a stress factor is considered. The framework for maximal coupling of time-inhomogeneous Markov chains is investigated, and as a result a theorem on the stability of expectations of a function on a Markov chain is proved. Numerical examples, such as a valuation of the impact of stress factors on the widow[er]’s pension price, are considered.

Keywords

Natural Stress Factors Time-inhomogeneous Markov Chain Pendent Price Maximum Coupling Actuator Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Bowers, N., Gerber, H., Hickman, J., Jones, D., Nesbitt, C.: Actuarial Mathematics. Society of Actuaries, Itasca, Ill (1986)zbMATHGoogle Scholar
  2. 2.
    Doeblin, W.: Expose de la theorie des chaines simples constantes de Markov a un nomber fini d’estats. Mathematique de l’Union Interbalkanique 2, 77–105 (1938)Google Scholar
  3. 3.
    Douc, R., Moulines, E., Rothenthal, J.S.: Quantitative bounds on convergence of time-inhomogeneous Markov chains. Ann. Appl. Prob. 14(4), 1643–1665 (2004)CrossRefzbMATHGoogle Scholar
  4. 4.
    Douc, R., Moulines, E., Rosenthal, J.S.: Quantitative bounds for geometric convergence rates of Markov chains. Ann. Appl. Probab. 14, 1643–1664 (2004b)CrossRefzbMATHMathSciNetGoogle Scholar
  5. 5.
    Douc, R., Moulines, E., Soulier, P.: Practical drift conditions for subgeometric rates of convergence. Ann. Appl. Probab. 14, 1353–1377 (2004)CrossRefzbMATHMathSciNetGoogle Scholar
  6. 6.
    Douc, R., Moulines, E., Soulier, P.: Computable convergence rates for subgeometrically ergodic Markov Chains. Bernoulli 13(3), 831–848 (2007)CrossRefzbMATHMathSciNetGoogle Scholar
  7. 7.
    Douc, R., Fort, G., Guillin, A.: Subgeometric rates of convergence of f-ergodic strong Markov processes. Stoch. Process. Appl. 119, 897–923 (2009)CrossRefzbMATHMathSciNetGoogle Scholar
  8. 8.
    Dublin, L.I., Lotka, A.J.: Length of Life, vol. 400. The Ronald Press, New York (1936)Google Scholar
  9. 9.
    England, Interim life tables, 1980–82 to 2008–2010. UK office for national statistics. http://ons.gov.uk/ons/rel/lifetables/interim-life-tables/2008-2010/rft-ilt-eng-2008-10.xls
  10. 10.
    Golomoziy, V., Kartashov, N., Kartashov, I.: Markov model approach for stress-tests in insurance pricing. Manuscript (2013)Google Scholar
  11. 11.
    Golomoziy, V.V.: Stability of time-inhomogeneous Markov chains. Visnik Kyivskogo universitetu. Ser. Phys. Math. (in Ukr) 4, 10–15 (2009)Google Scholar
  12. 12.
    Golomoziy, V.V.: Subgeometrical estimate for stability for time-inhomogeneous Markov chians. Teoria Imovirnostey ta matematichna statistica 81, 31–46 (2010)Google Scholar
  13. 13.
    Jarner, S.F., Roberts, G.O.: Polynomial convergence rates of Markov chains. Ann. Appl. Probab. 12, 224–247 (2001)MathSciNetGoogle Scholar
  14. 14.
    Kartashov, N. V., Golomoziy, V.V.: Maximal coupling and stability of discrete Markov chains I, II. Theor. Probab. Math. Statist. 87, 65–78 (2013)Google Scholar
  15. 15.
    Kartashov, N.V.: Strong Stable Markov Chains, vol. 441, p. 138. VSP, Utrecht (1996)Google Scholar
  16. 16.
    Kartashov, N.V.: Criteria for uniform ergodicity and strong stability of Markov chains with a common phase space. Theory Probab. Appl. 30, 71–89 (1985)zbMATHGoogle Scholar
  17. 17.
    Kartashov, N.V.: Inequalities in theorems of ergodicity and stability for Markov chains with a common phase space. Theory Probab. Appl. 30, 247–259 (1985)CrossRefGoogle Scholar
  18. 18.
    Kartashov, N.V.: The ergodicity and stability of quasi-homogeneous Markov semigroups of operators. Theor. Probab. Math. Statist. 72, 59–68 (2006)CrossRefMathSciNetGoogle Scholar
  19. 19.
    Kartashov, N.V., Golomoziy, V.V.: Average coupling time for independent discrete renewal processes. Teoria imovirnostey ta matematichna statistica 84, 78–85 (2011)Google Scholar
  20. 20.
    Lindvall, T.: Lectures on the Coupling Method, vol. 441, p. 237. Dover publication, New York (2002)Google Scholar
  21. 21.
    Mayn, S.P., Tweedie, R.L.: Markov Chains and Stochastic Stability, vol. 441, p. 552. Springer, New York (1993)Google Scholar
  22. 22.
    Nummelin, E.: A splitting technique for Harris recurrent chains. Z. Wahrscheinlichkeitstheorie Verw. Geb. 43, 309–318 (1978)CrossRefzbMATHMathSciNetGoogle Scholar
  23. 23.
    Nummelin, E., Tweedie, R.L.: Geometric ergodicity and R-positivity for general Markov chains. Ann. Probab. 6, 404–420 (1978)CrossRefzbMATHMathSciNetGoogle Scholar
  24. 24.
    Nummelin, E., Tuominen, P.: Geometric ergodicity of Harris recurrent Markov chains with applicatoins to renewal theory. Stoch. Proc. Appl. 12, 187–202 (1982)CrossRefzbMATHMathSciNetGoogle Scholar
  25. 25.
    Nummelin, E.: General Irreducible Markov Chains and Nonnegative Operators. Cambridge University Press, Cambridge (1984)CrossRefGoogle Scholar
  26. 26.
    Spreeuw, J., Owadally, I.: Investigating the broken-heart effect: a Model for short-term dependence between the remaining lifetimes of joint lives. Ann. Actuar Sci 7, 236–257 (2013)CrossRefGoogle Scholar
  27. 27.
    Thorisson, H.: Coupling, Stationarity, and Regeneration, vol. 490. Springer, New York (2000)Google Scholar
  28. 28.
    Trowbridge, C. Mortality rates by marital status. Trans. Soc. Actuar. 46 (1994)Google Scholar
  29. 29.
    Tuominen, P., Tweedie, R.: Subgeometric rates of convergence of f-ergodic Markov chains. Adv Appl. Probab. 26, 775–798 (1994)CrossRefzbMATHMathSciNetGoogle Scholar
  30. 30.
    Tweedie, R.L., Corcoran, J.N.: Perfect sampling of ergodic Harris chains. Ann. Appl. Probab. 11(2), 438–451 (2001)CrossRefzbMATHMathSciNetGoogle Scholar
  31. 31.
    Wolthuis, H.: Life Insurance Mathematics. The Markovian Model. CAIRE, Brussels (Education Series) (1984)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Taras Shevchenko National University of KyivKyivUkraine

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