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

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

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