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Year 2020, Volume: 3 Issue: 1, 207 - 214, 15.12.2020

Veli Bayramov , Afaq Abdullayeva Rovshan Aliyev

Abstract

References

  • 1 R.T. Aliyev, Asymptotic expansions for the first four moments of Sparre Andersen risk process, Transactions of NAS Azerbaijan Vol. XXXVI, 3(2016), 58-66.
  • 2 R. Aliyev, Second-order asymptotic expansion for the ruin probability of the Sparre Andersen risk process with reinsurance and stronger semiexponential claims, International Journal of Statistics and Actuarial Science, 1(2) (2017), 40-45.
  • 3 R. Aliyev, V. Bayramov, On the asymptotic behaviour of the covariance function of the rewards of a multivariate renewal-reward process, Statistics and Probability Letters, 127 (2017), 138-149.
  • 4 S. Asmussen, Ruin Probabilities, World Scientific. 2000, 620 p.
  • 5 A. Borovkov, Probability Theory, M.: URSS, 2009.
  • 6 M. Brown, H.A. Solomon, Second-order approximation for the variance of a renewal reward process, Stochastic Process. Appl., 3 (1975), 301-314.
  • 7 D.C. Dickson, H.R. Waters, Reinsurance and ruin, Insurance: Mathematics and Economics, 19 (1996), (1), 61-80.
  • 8 D.C. Dickson, H.R. Waters, Relative reinsurance retention levels, ASTIN Bulletin, 27(2) (1997), 207-227.
  • 9 D. Dickson, Proportional Reinsurance, Encyclopedia of Actuarial Science, 2006.
  • 10 C. Stone, On characteristic function and renewal theory, Trans. Amer. Math. Soc., 120 (2) (1965), 327-342.

On the Asymptotic Expansions for the Expected Value and Variance of the Reinsurance Surplus Process

Year 2020, Volume: 3 Issue: 1, 207 - 214, 15.12.2020

Veli Bayramov , Afaq Abdullayeva Rovshan Aliyev

Abstract

In this paper, we consider the reinsurance surplus process. Depending on the type of the reinsurance we obtain formulas for the distribution functions and moments of claims in reinsurance surplus process, then using these moments we give the asymptotic results for the mathematical expectation and variance in each type of the reinsurance. Then we give numerical examples to compare the values of mathematical expectation and variance when there is no reinsurance and when the insurer effects reinsurance.

Keywords

Reinsurance Surplus process Asymptotic expansion Mathematical expectation Variance Renewal process Renewal-reward process

References

  • 1 R.T. Aliyev, Asymptotic expansions for the first four moments of Sparre Andersen risk process, Transactions of NAS Azerbaijan Vol. XXXVI, 3(2016), 58-66.
  • 2 R. Aliyev, Second-order asymptotic expansion for the ruin probability of the Sparre Andersen risk process with reinsurance and stronger semiexponential claims, International Journal of Statistics and Actuarial Science, 1(2) (2017), 40-45.
  • 3 R. Aliyev, V. Bayramov, On the asymptotic behaviour of the covariance function of the rewards of a multivariate renewal-reward process, Statistics and Probability Letters, 127 (2017), 138-149.
  • 4 S. Asmussen, Ruin Probabilities, World Scientific. 2000, 620 p.
  • 5 A. Borovkov, Probability Theory, M.: URSS, 2009.
  • 6 M. Brown, H.A. Solomon, Second-order approximation for the variance of a renewal reward process, Stochastic Process. Appl., 3 (1975), 301-314.
  • 7 D.C. Dickson, H.R. Waters, Reinsurance and ruin, Insurance: Mathematics and Economics, 19 (1996), (1), 61-80.
  • 8 D.C. Dickson, H.R. Waters, Relative reinsurance retention levels, ASTIN Bulletin, 27(2) (1997), 207-227.
  • 9 D. Dickson, Proportional Reinsurance, Encyclopedia of Actuarial Science, 2006.
  • 10 C. Stone, On characteristic function and renewal theory, Trans. Amer. Math. Soc., 120 (2) (1965), 327-342.
There are 10 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Veli Bayramov

Afaq Abdullayeva This is me

Rovshan Aliyev

Publication Date December 15, 2020
Acceptance Date October 13, 2020
Published in Issue Year 2020 Volume: 3 Issue: 1

Cite

APA Bayramov, V., Abdullayeva, A., & Aliyev, R. (2020). On the Asymptotic Expansions for the Expected Value and Variance of the Reinsurance Surplus Process. Conference Proceedings of Science and Technology, 3(1), 207-214.
AMA Bayramov V, Abdullayeva A, Aliyev R. On the Asymptotic Expansions for the Expected Value and Variance of the Reinsurance Surplus Process. Conference Proceedings of Science and Technology. December 2020;3(1):207-214.
Chicago Bayramov, Veli, Afaq Abdullayeva, and Rovshan Aliyev. “On the Asymptotic Expansions for the Expected Value and Variance of the Reinsurance Surplus Process”. Conference Proceedings of Science and Technology 3, no. 1 (December 2020): 207-14.
EndNote Bayramov V, Abdullayeva A, Aliyev R (December 1, 2020) On the Asymptotic Expansions for the Expected Value and Variance of the Reinsurance Surplus Process. Conference Proceedings of Science and Technology 3 1 207–214.
IEEE V. Bayramov, A. Abdullayeva, and R. Aliyev, “On the Asymptotic Expansions for the Expected Value and Variance of the Reinsurance Surplus Process”, Conference Proceedings of Science and Technology, vol. 3, no. 1, pp. 207–214, 2020.
ISNAD Bayramov, Veli et al. “On the Asymptotic Expansions for the Expected Value and Variance of the Reinsurance Surplus Process”. Conference Proceedings of Science and Technology 3/1 (December 2020), 207-214.
JAMA Bayramov V, Abdullayeva A, Aliyev R. On the Asymptotic Expansions for the Expected Value and Variance of the Reinsurance Surplus Process. Conference Proceedings of Science and Technology. 2020;3:207–214.
MLA Bayramov, Veli et al. “On the Asymptotic Expansions for the Expected Value and Variance of the Reinsurance Surplus Process”. Conference Proceedings of Science and Technology, vol. 3, no. 1, 2020, pp. 207-14.
Vancouver Bayramov V, Abdullayeva A, Aliyev R. On the Asymptotic Expansions for the Expected Value and Variance of the Reinsurance Surplus Process. Conference Proceedings of Science and Technology. 2020;3(1):207-14.
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