Conference Paper

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

Volume: 3 Number: 1 December 15, 2020
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Conference Proceedings of Science and Technology
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On the Asymptotic Expansions for the Expected Value and Variance of the Reinsurance Surplus Process

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

References

  1. 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. 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. 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. 4 S. Asmussen, Ruin Probabilities, World Scientific. 2000, 620 p.
  5. 5 A. Borovkov, Probability Theory, M.: URSS, 2009.
  6. 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. 7 D.C. Dickson, H.R. Waters, Reinsurance and ruin, Insurance: Mathematics and Economics, 19 (1996), (1), 61-80.
  8. 8 D.C. Dickson, H.R. Waters, Relative reinsurance retention levels, ASTIN Bulletin, 27(2) (1997), 207-227.

Details

Primary Language

English

Subjects

Engineering

Journal Section

Conference Paper

Authors

Afaq Abdullayeva This is me
Azerbaijan

Rovshan Aliyev
Azerbaijan

Publication Date

December 15, 2020

Submission Date

August 6, 2020

Acceptance Date

October 13, 2020

Published in Issue

Year 2020 Volume: 3 Number: 1

IZ

https://izlik.org/JA35GL83EH

Cite

RIS / Bibtex
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. https://izlik.org/JA35GL83EH
AMA
1.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):207-214. https://izlik.org/JA35GL83EH
Chicago
Bayramov, Veli, Afaq Abdullayeva, and Rovshan Aliyev. 2020. “On the Asymptotic Expansions for the Expected Value and Variance of the Reinsurance Surplus Process”. Conference Proceedings of Science and Technology 3 (1): 207-14. https://izlik.org/JA35GL83EH.
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
[1]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, Dec. 2020, [Online]. Available: https://izlik.org/JA35GL83EH
ISNAD
Bayramov, Veli - Abdullayeva, Afaq - Aliyev, Rovshan. “On the Asymptotic Expansions for the Expected Value and Variance of the Reinsurance Surplus Process”. Conference Proceedings of Science and Technology 3/1 (December 1, 2020): 207-214. https://izlik.org/JA35GL83EH.
JAMA
1.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, Dec. 2020, pp. 207-14, https://izlik.org/JA35GL83EH.
Vancouver
1.Veli Bayramov, Afaq Abdullayeva, Rovshan Aliyev. On the Asymptotic Expansions for the Expected Value and Variance of the Reinsurance Surplus Process. Conference Proceedings of Science and Technology [Internet]. 2020 Dec. 1;3(1):207-14. Available from: https://izlik.org/JA35GL83EH