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Articles

Berry-Esseen bounds for compound-Poisson loss percentiles

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Pages 519-534 | Received 25 Nov 2015, Accepted 20 Apr 2016, Published online: 02 Jun 2016

References

  • Antonio, K. & Plat, R. (2014). Micro-level stochastic loss reserving for general insurance. Scandinavian Actuarial Journal 7, 649–669.
  • Berry, A. C. (1941). The accuracy of the Gaussian approximation to the sum of independent variables. Transactions of the American Mathematical Society 49, 122–136.
  • Esseen, C.-G. (1942). On the Liapunoff limit of error in the theory of probability. Arkiv för Matematik, Astronomi och Fysik A28(9), 1–19.
  • Esseen, C.-G. (1956). A moment inequality with an application to the central limit theorem. Scandinavian Actuarial Journal 39, 160–170.
  • Ekheden, E. & Hössjer, O. (2014). Pricing catastrophe risk in life (re)insurance. Scandinavian Actuarial Journal 4, 352–367.
  • Korolev, V. Y. & Shevtsova, I. G. (2010a). Sharpened upper bounds for the absolute constant in the Berry–Esseen inequality for mixed Poisson random sums. Doklady Mathematics 81(2), 180–182.
  • Korolev, V. Y. & Shevtsova, I. G. (2010). An improvement of the Berry–Esseen inequality with applications to Poisson and mixed Poisson random sums. Scandinavian Actuarial Journal 2012(2), 81–105. DOI: 10.1080/03461238.2010.485370.
  • Shevtsova, I. G. (2010). The lower asymptotically exact constant in the central limit theorem. Doklady Mathematics 81(1), 83–86.
  • Shevtsova, I. G. (2011). On the asymptotically exact constants in the Berry–Esseen–Katz inequality. Theory of Probability and its Applications 55(2), 225–252.
  • Shevtsova, I. G. (2014a). On the absolute constants in the Berry–Esseen-type inequalities. Doklady Mathematics 89(3), 378–381.
  • Shevtsova, I. G. (2014b). On the accuracy of the normal approximation to compound Poisson distributions. Theory of Probability and its Applications 58(1), 1–30.
  • Zolotarev, V. M. (1967a). A sharpening of the inequality of Berry–Esseen. Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete 8, S332–S342.
  • Zolotarev, V. M. (1967b). Some inequalities in probability theory and their application in sharpening the Lyapunov theorem. Soviet Mathematics – Doklady 8, 1427–1430.

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