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Dergiler / Conference Proceedings of Science and Technology / 2026 / Cilt: 3 Sayı: 1

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

Veli Bayramov(Baku State University)
Afaq Abdullayeva(Baku State University)
Rovshan Aliyev(Baku State University)
Sayfa
207–214
Yayın Tarihi
2020-12-15
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

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.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:In this paper, we consider the reinsurance surplus process.
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Temel Bulgular & Veri: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.
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Sonuç & Katkı: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.
🔬Tür:Konferans Bildirisi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Reinsurance · Surplus process · Asymptotic expansion

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.

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Bu Makaleye Atıf Yap

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, Cilt: 3 Sayı: 1, 207–214. https://ajindex.com/articles/1648734

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Kaynakça (10)

  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.
  9. 9 D. Dickson, Proportional Reinsurance, Encyclopedia of Actuarial Science, 2006.
  10. 10 C. Stone, On characteristic function and renewal theory, Trans. Amer. Math. Soc., 120 (2) (1965), 327-342.