Akademik Veri Yönetim Sistemi
European Actuarial Journal Conference 2024, Lisbon, Portekiz, 9 - 11 Eylül 2024, ss.45-46, (Özet Bildiri)
The primary objective of insurance companies is to protect policyholders against potential losses in exchange
for a specified premium [1]. To achieve this, it is essential to charge a fair premium and maintain adequate
capital and reserves. Accurate prediction of claim frequency and amounts, both individual and aggregate,
is crucial as it directly impacts pricing and reserving strategies. Over the past four decades, Generalized
Linear Modeling (GLM) has become vital for actuaries in rate-making, pricing, and reserving due to its
flexible framework in parameter and model selection [2, 3].
Heterogeneity in statistical modeling arises from deviations due to unobservable risk factors. In claim
modeling, random effects represent unobserved risk factors, while fixed effects represent observed ones.
The Generalized Linear Mixed Model (GLMM) is a recognized approach for managing this heterogeneity,
though random effects can increase the correlation variance of the dependent variable [4, 3]. Studies have
also explored heterogeneity in credibilit or tariff models, often focusing on time-varying heterogeneity over
unobservable risk factors, using extensions like the state-space model (SSM) [5, 6].
Serial correlation in claim modeling refers to the relationship between claim frequencies or severities
and their lagged versions, which can increase the variance of demand frequencies. GLMMs and time series
approaches in longitudinal settings have been proposed to manage this serial correlation [7, 3].
This study aims to demonstrate, through extensive validation, that the proposed method outperforms
existing models in addressing actuarial loss function challenges. The new approach enhances adaptability,
flexibility, accuracy, and applicability, potentially uncovering complex hidden risk factors. Simulation studies and real-life dataset applications were used to evaluate the model’s performance. The primary goal is to
illustrate how the model effectively represents heterogeneity from unobserved risk factors.
Our findings reveal that heterogeneity from unobserved risk factors is represented by three discrete hidden states in the analyzed dataset. Extensive validation confirms that the proposed method surpasses existing
models in handling actuarial claims modeling complexities. Real-life examples show that the new method
yields superior results by effectively representing heterogeneity and serial correlation based on unobservable
risk factors. This innovative approach offers robust solutions to traditional actuarial claim model challenges,
significantly advancing actuarial science
References
[1] Rocca G (2019) Predictive methods for calculating the non-life insurance premium (Doctoral dissertation, Politecnico di Torino).
[2] Renshaw AE (1994) Modelling the claims process in the presence of covariates. ASTIN Bulletin: the Journal of the IAA 24(2):265–285.
[3] Denuit M, Trufin J (2019) Effective statistical learning methods for actuaries, Vol.795. Springer, Berlin.
[4] McCulloch CE, Searle SR, Neuhaus JM (2001) Generalized, linear, and mixed models, Vol.325. John Wiley & Sons, New York.
[5] Pinquet J, Guillen M, Bolance C (2001) Allowance for the age of claims in bonus-malus systems. ASTIN Bulletin: The Journal of the IAA 31(2):337–348.
[6] Pinquet J (2020). Poisson models with dynamic random effects and nonnegative credibilities per period. ASTIN Bulletin: The Journal of the IAA 50(2):585–618.
[7] Avanzi B, Wong B, Yang X (2016) A micro-level claim count model with overdispersion and reporting delays. Insurance: Mathematics and Economics 71:1–14.