Hasar Modellerine Alternatif Yaklaşım: Heterojenlik ve Seri Korelasyon için Kapsamlı Bir Çözüm

Abstract

This study aims to enhance the modeling process of actuarial loss functions by introducing an innovative approach to address challenges related to heterogeneity and serial correlation. Traditional models like Generalized Linear Mixture Models (GLMM) and time series methodologies have limitations, particularly concerning variance inflation and inflexibility due to inherent assumptions.

To address these issues, this research proposes the use of Generalized Linear Model Hidden Markov Models (GLM-HMM) at the individual level. HMMs effectively capture heterogeneity through hidden states and incorporate serial correlation via transition probabilities. This approach promises greater flexibility, accuracy, and applicability, potentially revealing patterns that conventional models cannot discern.

The motivation behind this novel approach is to offer a comprehensive solution to actuarial modeling challenges. The proposed model will undergo rigorous validation across diverse datasets, comparing its performance against existing models to establish its superiority.

One significant application of HMMs in actuarial science is in the calculation of premium risk, a critical component of internal models like Solvency II. HMMs can identify hidden states within specific policy years, improving premium risk estimates and facilitating the development of more robust models. This capability is particularly beneficial for actuarial rate setting and pricing, allowing for more detailed analyses and the identification of unobservable heterogeneity.

HMMs enable insurers to better understand risk factors by identifying hidden states behind observable variables such as policy amounts, claim frequencies, and loss amounts. This understanding allows for more accurate premium risk estimation and dynamic risk management strategies. Additionally, HMMs support the calculation of separate premium risks for insureds with different risk profiles, leading to fairer and more precise pricing policies that enhance the competitiveness of insurance companies.

By modeling unobservable heterogeneity, HMMs contribute significantly to actuarial rate setting and pricing. They allow for differentiated premium calculations based on risk groups, fostering fairer pricing policies and increasing market competitiveness. This capability to create risk-aligned pricing policies can help insurance companies expand their market share and optimize their risk management strategies in a dynamic environment. Overall, HMMs offer a robust, accurate, and flexible tool for improving premium risk estimates and actuarial modeling practices.