Opuscula Math. 38, no. 6 (2018), 871-882

Opuscula Mathematica

Estimation of the distortion risk premium for heavy-tailed losses under serial dependence

Hakim Ouadjed

Abstract. In the actuarial literature, many authors have studied estimation of the reinsurance premium for heavy tailed i.i.d. sequences, especially for the Proportional Hazard (PH) due to Wang. The main aim of this paper is to extend this estimation for heavy tailed dependent sequences satisfying some mixing dependence structure. In this study we prove that the new estimator is asymptotically normal. The behavior of the estimator is examined using simulation for MA(1) process.

Keywords: extreme value theory, mixing processes, tail index estimation.

Mathematics Subject Classification: 60G70, 62G32.

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  • Hakim Ouadjed
  • Department of Gestion, Faculty of Science of Gestion, Economic and Commerce, Mustapha Stambouli University, Mascara, Algeria
  • Mathematics Laboratory, Djillali Liabes University of Sidi Bel Abbes, Algeria
  • Communicated by Marek Rutkowski.
  • Received: 2017-06-05.
  • Revised: 2018-04-28.
  • Accepted: 2018-04-29.
  • Published online: 2018-07-05.
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Cite this article as:
Hakim Ouadjed, Estimation of the distortion risk premium for heavy-tailed losses under serial dependence, Opuscula Math. 38, no. 6 (2018), 871-882, https://doi.org/10.7494/OpMath.2018.38.6.871

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