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Nonparametric Estimation of Net Premium Functionals for Different Statuses in Collective Life Insurance

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Information Technologies and Mathematical Modelling (ITMM 2014)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 487))

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Abstract

The nonparametric estimators of net premiums in collective models of insurance for the different statuses of collective life insurance are proposed. The asymptotic normality and mean square convergence of the proposed estimates are proved. The main parts of asymptotic mean square errors (MSEs) for estimators of net premiums are found. The results of simulations show that the nonparametric estimates are just as good in practice.

Supported by Russian Foundation for Basic Research, projects 13-08-00744, Tomsk State University Competitiveness Improvement Program, and the project “Goszadanie Minobrnauki Rossii”.

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References

  1. Bowers, N.L., Gerber, H.U., Hickman, J.C., Jones, D.A., Nesbitt, C.J.: Actuarial Mathematics, 624p. The Society of Actuaries, Itasca (1986)

    Google Scholar 

  2. Bloink, R.: Premium Financed Surprises: Cancellation of Indebtedness Income and Financed Life Insurance. Tax Lawyer 63(3), 223–227 (2010)

    Google Scholar 

  3. Buhlmann, H.: The general economic premium principle. ASTIN Bulletin 14, 13–21 (1984)

    Google Scholar 

  4. Dong, Y.: Fair Valuation of Life Insurance Contracts under a Correlated Jump Diffusion Model. ASTIN Bulletin 41(2), 429–447 (2011)

    MATH  MathSciNet  Google Scholar 

  5. Faust, R., Schmeiser, H., Zemp, A.: A Performance Analysis of Participating Life Insurance Contracts. Insurance: Mathematics and Economics 51(1), 158–171 (2013)

    MathSciNet  Google Scholar 

  6. Maurer, R., Rogalla, R., Siegelin, I.: Participating Payout Life Annuities: Lessons from Germany. ASTIN Bulletin 43(2), 159–187 (2013)

    Article  MATH  Google Scholar 

  7. Schmeiser, H., Wagner, J.: A Joint Valuation of Premium Payment and Surrender Options in Participating Life Insurance Contracts. Insurance: Mathematics and Economics 49(3), 580–596 (2011)

    MATH  MathSciNet  Google Scholar 

  8. Sliwinski, A., Michalski, T., Roszkiewicz, M.: Demand for Life Insurance–An Empirical Analysis in the Case of Poland. The Geneva Papers on Risk and Insurance 38, 62–87 (2013)

    Article  Google Scholar 

  9. Aase, K.K.: Premiums in a dynamic model of a reinsurance market. Scandinavian Actuarial Journal, 134–160 (1993)

    Google Scholar 

  10. Arora, N., Arora, P.: Insurance Premium Optimization: Perspective of Insurance Seeker and Insurance Provider. Journal of Management and Science 4(1), 43–53 (2014)

    Google Scholar 

  11. Bohnert, A., Gatzert, N.: Analyzing Surplus Appropriation Schemes in Participating Life Insurance from the Insurer’s and the Policyholder’s Perspective. Insurance: Mathematics and Economics 50(1), 64–78 (2012)

    MATH  MathSciNet  Google Scholar 

  12. Gatzert, N.: Asset Management and Surplus Distribution Strategies in Life Insurance: An Examination with Respect to Risk Pricing and Risk Measurement. Insurance: Mathematics and Economics 42(2), 839–849 (2008)

    MATH  MathSciNet  Google Scholar 

  13. Gatzert, N., Wesker, H.: The Impact of Natural Hedging on a Life Insurer’s Risk Situation. Journal of Risk Finance 13(5), 396–423 (2012)

    Article  Google Scholar 

  14. Huang, H., Lee, Y.-T.: Optimal Asset Allocation for a General Portfolio of Life Insurance Policies. Insurance: Mathematics and Economics 46(2), 271–280 (2010)

    MATH  MathSciNet  Google Scholar 

  15. Rocio, P., Aguilar, C., Xu, C.: Design Life Insurance Participating Policies using Optimization Techniques, International Journal of Innovative Computing. Information and Control 6(4), 1655–1666 (2010)

    Google Scholar 

  16. Gerber, H.U.: Principles of Premium Calculation and Reinsurance. In: Transactions of the 21st International Congress of Actuaries, pp. 137–142 (1980)

    Google Scholar 

  17. Koshkin, G.M.: Nonparametric Estimation of Moments of Net Premium in Life Insurance. In: Aivazyan, S.A., Kharin, Y.S. (eds.) Computer Data Analysis and Modeling: Proceedings of the Fifth International Conference, June 8-12. A-M, vol. 1, pp. 148–153. BSU, Minsk (1998)

    Google Scholar 

  18. Koshkin, G.M., Lopukhin, Y.N.: On estimation of net premium in collective life insurance. In: Proceedings of the 5th Korea-Russian International Symposium on Science and Technology, KORUS 2001, June 26-July 3, vol. 2, pp. 296–299. Tomsk Polytechnic University, Tomsk (2001)

    Chapter  Google Scholar 

  19. Koshkin, G.M., Lopukhin, Y.N.: Estimation of Net Premiums in Collective Models of Life Insurance. In: XIth Annual International AFIR Colloquium, September 6-7, vol. 2, pp. 447–457. Canadian Institute of Actuaries, Toronto (2001)

    Google Scholar 

  20. Koshkin, G.M., Lopukhin, Y.N.: Nonparametric Estimation of Net Premiums in Collective Insurance. In: Aivazyan, S., Kharin, Y., Rieder, H. (eds.) Computer Data Analysis and Modeling: Robustness and Computer Intensive Methods: Proceedings of the Sixth International Conference, Minsk, September 10-14. A-K, vol. 1, pp. 236–241. BSU, Minsk (2001)

    Google Scholar 

  21. Dobrovidov, A.V., Koshkin, G.M., Vasiliev, V.A.: Non-parametric State Space Models, Heber, UT 84032, USA, p. 501. Kendrick Press, Inc. (2012)

    Google Scholar 

  22. Ibragimov, I.A., Khas’minski, R.Z.: Asymptotic Theory of Estimation, p. 528. Nauka, Moskva (1979) (in Russian)

    Google Scholar 

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Author information

Authors and Affiliations

  1. National Research Tomsk State University, Lenin Avenue, 36, 634050, Tomsk, Russia

    Gennady Koshkin & Yaroslav Lopukhin

Authors
  1. Gennady Koshkin
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  2. Yaroslav Lopukhin
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Editor information

Editors and Affiliations

  1. Department of Applied Mathematics and Computer Science, Belarusian State University, 220030, Minsk, Belarus

    Alexander Dudin

  2. Tomsk State University, Tomsk, Russia

    Anatoly Nazarov

  3. Kemerovo State University, Anzhero-Sudzhensk, Russia

    Rafael Yakupov

  4. National Research Tomsk State University, 634050, Tomsk, Russia

    Alexander Gortsev

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Koshkin, G., Lopukhin, Y. (2014). Nonparametric Estimation of Net Premium Functionals for Different Statuses in Collective Life Insurance. In: Dudin, A., Nazarov, A., Yakupov, R., Gortsev, A. (eds) Information Technologies and Mathematical Modelling. ITMM 2014. Communications in Computer and Information Science, vol 487. Springer, Cham. https://doi.org/10.1007/978-3-319-13671-4_27

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  • DOI: https://doi.org/10.1007/978-3-319-13671-4_27

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-13670-7

  • Online ISBN: 978-3-319-13671-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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