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A New Approach for Enhancing Aggregate Loss Modeling
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AI
DOI：10.1080/10920277.2025.2603265.png)
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Abstract
En 中文
The aggregate loss distribution plays an important role in many actuarial applications, providing key insights into the risk profile of an insurance portfolio. Traditionally, a detailed assessment of this distribution relied either on various approximation methods or on recursive or convolution methods that necessitate the discretization of the loss distribution. In contrast to these approaches, this article introduces a mixture model for direct estimation of the aggregate loss distribution, where policyholders are grouped based on the number of claims they generate. The claim frequency distribution is explicitly accounted for within this model using the mixture weights, for example, based on a truncated Poisson distribution. Theoretical support for this mixture model is provided along with closed-form expressions for risk measures and the net stop-loss premium derived considering two severity distributions: gamma and lognormal. Furthermore, five existing approximation methods (normal, normal-power II, lognormal, gamma, and inverse Gaussian) are extended through the derivation of explicit formulas for risk measures and the net stop-loss premium. The proposed method is evaluated against these five approximation methods, as well as recursive and convolution methods, using both real-world data on French motor losses and simulation studies. The results indicate a suitable performance of the proposed approach, suggesting a potential shift away from traditional approximation and discretization-based methods.
Keywords:
CLAIMS
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