Credibility Theory Under the Least Squared Relative Loss Function

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ABSTRACTThe classical Bühlmann model employs a least squared loss criterion that penalizes pricing errors equally across all risk classes. In contrast, this paper develops a new credibility theory based on the least squared relative loss (LSRL) function to address scenarios where the classical approach may fall short. We derive explicit expressions of LSRL‐based credibility estimators, including non‐parametric versions and Bühlmann–Straub extensions. Through a comparative study, we illustrate the real‐world applicability of the LSRL estimator across different scenarios, highlighting its advantages and limitations in comparison to the classical model. Additionally, we explore different LSRL formulations to provide deeper insights into their practical viability.