Estimation of distortion risk premiums in reinsurance under random right-censoring

Year 2025, Volume: 54 Issue: 4, 1501 - 1517, 29.08.2025

Jihane Abdelli , Brahimi Brahim

https://doi.org/10.15672/hujms.1608715

Abstract

This paper focuses on the estimation of distortion risk premiums for large reinsurance claims in the context of random right-censoring. We build an asymptotically normal estimator which is based on censored observations for Pareto-type distributions which represent heavy-tailed risks. The method combines semi-parametric extremes with extreme value theory to yield coherent premium estimates under the most challenging claim data scenarios. The provided simulations in conjunction with comprehensive censoring contexts and variances in tail heaviness illustrates the estimator's robustness and outperformance. Empirical assessment using Norwegian fire claims together with cybersecurity breach datasets adds to the proven value of the methodology. This work presents a robust approach to the estimation of risk at extreme values under censoring that directly impacts excess-of-loss reinsurance contracts and the solvency capital requirements defined by the risk decisions made by actuaries and managerial stakeholders.

Keywords

Actuarial science , censoring , distortion risk premium , Pareto-type distribution , reinsurance premium , tail index

Thanks

Please find enclosed my paper, co-authored by Brahimi brahim Entitled: “Estimation of Distortion Risk Premiums in reinsurance under random right-censoring”, which I submit for possible publication to Hacettepe Journal of Mathematics and Statistics Conflicts of Interest: The authors declare no conflicts of interest regarding the publication of this paper. Should you have any questions or require further information concerning this submission, please contact me at the address listed below. Best regards, Jihane Abdelli, PhD, Professor Laboratory of Applied Mathematics Mohamed Khider Universy of Biskra, PO Box 145 RP, Biskra, 07000, Algeria

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